Obviously her father wasn't called Ludgate as you realise.
I've searched for Spark(e) on the apprentice rolls here https://www.londonroll.org/search and there are only three entries for Drapers: William Spark - New Apprentice 1545, William Spark - Freeman 1555 and William Sparke - Master 1565. These are almost certainly the same person and I would therefore suggest the likely father of Valentia.
Apprentices couldn't marry so we should look for a marriage from 1555 onwards and a William Sparke married an Elizabeth Ratcliff 21 June 1562. Irritatingly it's not at the same church but at St Vedast, Foster Lane which is just the other side of St. Paul's. "England Marriages, 1538–1973 ," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:V52H-LY5 : 10 February 2018), William Sparke and Elizabeth Ratcliff, 21 Jun 1562; citing Saint Vedast Foster Lane And Saint Michael Le Querlo,London,London,England, reference , index based upon data collected by the Genealogical Society of Utah, Salt Lake City; FHL microfilm 942 B4HA V. 30
Of course this is just speculation, not proof. One mystery would be why Lionel and Valentia called their eldest son Richard when both parents' fathers were called William - although their second son on wikitree has a middle initial W. Their first daughter was Elizabeth which would fit.