The identification of Francis Lucy, father in law (in DNB) of Sir Philip Meadows, with the son of Sir Thos Lucy was made by RCLPL.  As yet no confirmation from other sources.

In Burke's General Armory the Lucy arms are:
  Gules semee of crosses crosslet three lucies haurient or.

These are the arms impaled with Meadows on the infamous tankard...   Sounds like half of a confirmation.

TFPL, 3 Oct 2001: I found an item on him in the CDROM of Foster's Alumni Oxonienses which, with the name of his wife, further resolves the above problem of his identity:

"Lucy, Francis, eq. aur. fil. TRINITY COLL., matric 5 May, 1615, aged 15; bar-at-law, Lincoln's Inn, 1623 (as 6s Sir Thomas, late of Charlcote, co Warwick kt, deceased), licensed 9 Dec., 1630 to marry Elizabeth, daughter of Bevill Molesworth, of Hoddesdon, Herts, spinster; M.P. Warwick 1624-5, 1625, 1626, 1628-9; brother of George 1607, Thomas 1601, Richard 1607 and William 1613.  See Foster's Judges and Barristers."
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TFPL, March 2003

In 1894 Burke's Peerage for the first time reported, on the earldom of Manvers, that Francis Lucy was of the Charlcote family:

"Sir Philip Medows, ..., m. in 1661, Constance, 2nd dau. and co-heir of Francis Lucy, Esq, youngest brother of Sir Thomas Lucy of Charlcote..."

In 1939 this was still being recorded.  The earldom is now extinct and I know of noone to approach of that family for any further confirmation.

A possibility is the entry for Francis Lucy in the History of the House of Commons but the Society of Genealogists did not have the volume required (if, indeed, it has been published yet).
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TFPL, July 2003:

From The Members of Parliament 1213-1874, pub 1878, he was in the following parliaments for Warwick Borough:
23 Jan 1632-4
10 May 1625
(NA) 1625-6
3 Apr 1628
30 Jan 1628/9

This means that he will be in the 1604-1629 volume which was 90% complete in April 2002.  Sounds like not far away, what with proof checking and indexing.
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TFPL, August 2003:
In the "History of Parliament, House of Commons 1660-1690, Vol II, C-L", the entry for Sir Fulk Lucy says (a) he was sixth s, of Sir Thos Lucy of Charlecote and Alice Spencer and (b) that "Lucy's support [for some bill] might be gained through the influence of Philip Meadows, the Cromwellian diplomat and a distant connexion by marriage".  In fact this Fulk was first cousin once removed of Phil Meadows' wife Constance.
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TFPL, Oct 2003: Frustratingly he is in the Warks vis'n of 1682 but his wife and children are omitted...  The vis'n said: "Francis Lucy of the Citty of Westmr Esqr, now living ao 1682.".
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TFPL, Dec 2005: Bingo! At last some (secondary) evidence to confirm that he was of the Lucies of Charlecote.  From the text of the History of Parliament, when his elder brother Richard died in 1667, he became the guardian of his heir, Kingsmill; later on he had to put an Act through parliament to sort out young Kingsmill’s marriage settlement.  Someone may confirm this by studying Richard’s will and this Private Act of Parl but I am quite satisfied for now.
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See his will that he and Elizabeth had three daughters:
1. N.N. (d. bef. 1687) who m. Sir Edward Akins,
2. Constance m. Sir Philip Meadow,
3. Martha m. Samuel Eyre.

The same VCH volume reports they also had a son Richard who dsp and dvp.  Richard had married Rebecca and she m. (2) Sir Rowland Lytton.  However other reports from Burke, etc, have Rebecca marrying (2) Sir Richard Lucy, bt, brother to Francis.  CoKayne  in his Complete Baronetage, vol I, pp. 113-4, is very clear that Rebecca m. Sir Richard Lucy.
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The Parliament Trust reports that he was of Westminster and Brightwalton, Berks.
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From Collectanea Topographica et Genealoica:

Vol 4, p. 399: [Additions and Corrections to Vol 3] “P. 318. In the Hammersmith register occurs in the year 1686
                                         £ s d
  Buried Feb 4 Francis Lucy              0 8 0
  Sent me by Mis Lucy a G. (guinea)      1 1 6
  It appears from the same book that Mis Lucy paid the Minister, Mr John Wade, 1l. “Pewage” from lady-day 1685-6 to Lady-day 1686-7; and from the Register book of Benefactions it appears that in 1685 Francis Lucy, Esq. gave some land for the enlargement of the Chapelyard at Hammersmith. (Faulkner’s Fulham, p. 160.)  That the person buried was this gentleman is shown by the coffin-plate recently found in or near Hammersmith church, bearing this inscription: “Here lyeth ye body of Frances Lucy, Esq. youngest son of Sr Thomas Lucy of Charlecott, in ye county of Warwick.  Died January ye 30th in ye 90th yeare of his age, anno dom’ 1686-7.”  He was Member of parliament for Warwick, 1676-1685, and brother to Dr. William Lucy, bishop of St David’s 1660-1677.  Francis married in Feb 1631, Elizabeth, dau. and coh. of Bevill Molesworth, of Hoddesdon, co. Herts Esq. and left issue three daughters: 1. Elizabeth, mary. to Sir Edward Atkins, Baron of the Exchequer; 2. Constance, mary. to Sir Philip Meadows, Ambassador to Sweden, and was grandmother of the first Earl Manvers; and 3. Martha, mary. to Sir Samuel Eyre, Judge of the King’s Bench.  Sir Philip Meadows was buried at Hammersmith in 1718, as were others of his family (see vol. iii. p. 318).”
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From Visitation of England and Wales, Notes vol 5, p. 113:

“Francis Lucy of Fulham, co Middlesex, esquire (6th son of Sir Thomas Lucy of Charlcote, co Warwick, knight); of Trinity College, Oxford, matriculated 5 May 1615, aged 15; admitted to Lincoln’s Inn 4 May 1616, Barrister-at-law 1623; MP for Warwick 23 January 1623/4, 10 May 1625, and 3 April 1629; aged 28 9 December 1630; died, aged 89, 30 January, bur. at Hammersmith, co Middlesex, 4 February 1886/7. Will dated 7 September 1682, proved 15 February 1686/7 (P.C.C. 25 Foot)”
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From British History Online, in the VCH for Berks, Vol 4, pp. 48-51 on the parish of Brightwalton  there is a footnote on Francis Lucy’s will:

“P.C.C. 25 Foot. He left legacies to Sir Edward Atkins, kt., baron of the Exchequer, who had married his eldest daughter, lately deceased, to Sir Philip Meadow, kt., the husband of his second daughter Constance, and to Samuel Eyre, who had married his third daughter Martha.”
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His will reference from TNA’s website:

Will of Francis Lucy of Saint Martin in the Fields, Middlesex

Prerogative Court of Canterbury and related Probate Jurisdictions: Will Registers. Will of Francis Lucy of Saint Martin in the Fields, Middlesex.

Collection: Records of the Prerogative Court of Canterbury
Date range: 15 February 1687
Reference:  PROB 11/386/253
Subjects:   Wills and probate

The atual will confirms that probate was on 15th Feb 1687(-8).  Elizabeth Lucy was the sole executor.
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In his will he lists:

His wife Elizaberthm executor,
His elder daughter married to Sir Edward Atkins,
His second daughter, married to Sir Philip Meadows,
His youngest daughter, married to Samuel Eyre esq,
His sonne(s?),
Lady Lytton, relict of Sir Rowland Lytton, [and prior to that the widow of his eldest brother Sir Richard Lucy, bt],
His late brother the bishop of St David’s and his children,
His neice Michell,
Various staff and servants in his household.

The surprisin thing in all this is the mention of his son, named in Boyd’s London inhabitants as Richard who married Rebecca, dau & hr of Thomas Chapman of Wormley, relict of Sir Thomas Hayter.  On the other hand the History of Parliamnet says that his daughters were co-heirs.
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Gules three lucies or - Boutell's Heraldry, 1973 edition, p. 79 inc fig 198.

RCL P-L gives them as: Gules semée of crosses crosslets three lucies haurient argent.