Lynette was last seen at her mother's workplace - a supermarket on High Street at Penrith - on June 5, 1972.
Police have been told the teen arranged with her mum to be collected from her boyfriend's house at Penrith later that day, but she never arrived at his home.
A coronial inquest into her disappearance in 2001 found she most likely died on or about June 5, 1972.
The Unsolved Homicide Unit has been re-examining the case and the reward is being offered for information which leads to the arrest and conviction of any person responsible for her disappearance.
Detective Chief Inspector David Laidlaw said police believed Lynette was seen speaking with two males in a panel van near her house on Caloola Avenue, Penrith, formerly Kingswood Park, on the day she disappeared.
Police want to speak with anyone who lived in Caloola Avenue at that time in the hope they can help identify those men.
"We also believe a male who worked either in a bakery or doing bread deliveries and was known to Lynette may have assisted police initially, and urge him to come forward," Det Insp Laidlaw said on Wednesday.
Lynette's twin sister, Liana Stewart, said her family's grief has been "unimaginable".
"It never goes away and the hole in our hearts can never be repaired," she said.
"We know Lynette met with something sinister and is never coming back.
"The best we can hope for is someone who knows something will come forward so we can finally know what happened.
"It's too late for mum, who we lost two years ago, but we pray we get the answers, particularly for our 86-year-old dad."
