It sounds like it's a folk etymology, but it's true: tawdry is short for tawdry lace, which is short for St. Audrey's lace. Skeat says that tawdry lace referred to lace bought at St. Awdrey's fair, celebrated on October 17. Tawdry obviously underwent some perjoration, perhaps by association with cheap and showy lace. According to the OED, it is told that St. Audrey wore many necklaces, and died of a throat tumour, which was considered just retribution for her vanity.
The name Audrey is from Old English Æþelðryþ, which is composed of æþel "noble" and þryþ "power, strength". A cognate of þryþ is found in the -trude of Gertrude (from Old High German gēr "spear" and drūd "strength"). Æþel is from Proto-Indo-European *at-h₂el- "race, family", from *at- "over, beyond", and *h₂el- "to grow, nourish". See also Alice and edelweiss.