What is Lee Ashworth's goal in Broadchurch S2 E2-4?

The first half of series 2 of Broadchurch has a major subplot involving a witness and a suspect from DI Hardy's previous murder investigation in Sandbrook: Claire Ashworth testified that her husband Lee had been with her the night of the murder, but later recanted this testimony to DI Hardy. She later tells DS Miller that she had been drugged by Lee, and does not know what he did.

Lee Ashworth has been out of the country, presumably lying low after being accused (and possibly tried unsuccessfully) as a suspect in Pippa's murder. Early in series 2, he:

arrives in Broadchurch and tries to convince DI Hardy to reopen the case and exonerate him. Claire appears initially terrified of him, but soon appears compelled to restart their relationship. DS Miller and DI Hardy become increasingly suspicious of Claire as her story of the night of the girls' disappearance keeps changing.

So far, so good. Unfortunately, this doesn't make sense to me in light of the last episode of series 2, where it is revealed that:

Lee Ashworth slept with Lisa Newberry on the night of the murders. When they were discovered by Lisa's uncle Ricky Gillespie, Ricky pushed Lisa onto the floor, causing her to strike her head and die. They were witnessed after the murder by Pippa Gillespie, who tells Claire what she saw. Claire gives her Ricky's hip flask containing rohypnol, a date-rape drug, then convinces Lee to smother her with a pillow to prevent her naming Lee as Lisa's murderer. Finally, Claire hides the flask to use against Ricky in case he decides to go to the police.

Given all that, why was Lee Ashworth trying to get DI Hardy to reopen the Sandbrooke case at the start of series 2? Or am I misinterpreting their conversation?