The suspect in Houston’s notorious “Lovers’ Lane murders” has died in custody weeks after he was finally arrested for the 36-year-old double slayings. Floyd William Parrott, 64, was found unresponsive in his Nebraska prison cell on Tuesday while awaiting extradition back to Texas for allegedly slitting the throats of young lovebirds Cheryl Henry, 22, and Andy Atkinson, 21, in 1990. Parrot’s cause of death is under review but he appears to have killed himself, Harris County District Attorney Sean Teare told KHOU . A suspect has been charged with a 36-year-old double slaying in Houston known as the “Lovers’ Lane Murders.” KHOU 11 Parrott was busted in Lincoln, Nebraska, on March 25 and charged with the murders, finally breaking open a horrific cold case that scarred the Houston area for decades.  Prosecutors in Texas regret not being able to present their evidence in court but said they are still working the case — while probing another cold case linked to the Parrot.…