Burke (pg 365-366) and Oremod (p 19) both say she was the daughter of Algar, the Saxon, Earl of Mercia. According to Cockayne, which dedicates a whole Appendix to 'the Countess Lucy" (Complete Peerage, Volume VII, Appendix J), her parentage "is one of the unsolved puzzles of genealogy". It reports an early chronicle as saying that "she was a daughter of Aelfgar, Earl of Mercia, and niece or grandniece of Thorold, sometime Sheriff of co. Lincoln". HOWEVER, Cockayne also says "All that is certainly known is that she was niece of Robert Malet of Eye and of Alan of Lincoln, and that Thorold the Sheriff was a kinsman." He then reports the view that she was daughter of Thorold, Sheriff of Lincolnshire. There appear to be arguments for both theories, both of which make reference to the inheritance of various lands. Some 'serious' modern genealogists seem to lean strongly towards the view that she was daughter of Sheriff Thorold (Turold of Bucknell) by a daughter of William de Malet (Sanders, English Baronies, p. 18; Keats-Rohan, Domesday Descendants, p. 40, 247). The chart in Early Yorkshire Charters [ http://www.archive.org/details/earlyyorkshirech02farruoft ], Volume 2, pg 195 says Lucy is a kinswoman of Thorold, Sheriff of Lincoln.

from Genajourney.com
"The identity of Countess Lucy has been the subject of much attention by genealogists for literally hundreds of years. Two early sources state she was the daughter of Aelfgar, Earl of Mercia, and niece, or grandniece of Thorold, sometime Sheriff of Lincoln, but all that can [be] stated of her with certainty is that she was the niece of Robert Malet of Eye, and of Alan of Lincoln, and that Thorold the Sheriff of Lincoln was a kinsman. The link between Lucy and Aelfgar is the manor of Spalding in Lincoln, which was held by Aelfgar before the Conquest and subsequently held by Lucy's first husband, Ivo de Taillebois, in her right, at the time of Domesday. But chronology does not appear to justify the relationship of Lucy as daughter of Aelfgar, and the latter had only the known children Edwin, Morcar, and Aeldgitha. It appears more likely that the manor of Spalding passed from Aelfgar to Thorold, and then from Thorold to Lucy. Other manors of Thorold which passed to Lucy were Belchford, Scamblesby, Stenigot, Tetney, and Donington. She also held Alkborough, which had belonged, in the time of the Confessor, to William Malet, father of Lucy's uncle, Robert Malet. It is thereby surmised that her mother was a daughter of William Malet, and Alkborough may have been her maritagium. Thorold appears to have founded a cell at Spalding, subject to Crowland, but those charters, which would have been with the monks at Crowland, were destroyed by fire. So while the circumstantial evidence is compelling, this still does not prove Lucy's paternity, for her (unknown) father might have intervened as heir to Thorold."

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This has been settled in favor of Turold, Sheriff on Lincoln by Katherine Keats-Rohan: