What would improve their fortunes, then?
You'd need to make the Tories be even more of a trainwreck than IOTL. Here are a few ideas
-The Tories fall even harder when they lose under Major, either because the election comes sooner or something else, perhaps his affair with Edwina Currie, comes out
-Portillo makes it to the final ballot in 2001 and the stuff about his past homosexual experiences is enough for Ken Clarke to edge it. The Tories are in civil war for the next few years as Clarke can't reconcile his own moderate views with those of his backbenchers, and his is kicked out over he is opposition to Iraq, and replaced with IDS, and they proceed to do worse in 2005.
-There is a stronger, more organised left wing breakaway from the Tories than the Pro Euro Conservative Party, that eventually ends up entering into an alliance and/or merging with the Lib Dems. Or alternatively, a stronger Eurosceptic Party of the right that can peel off votes from the Tories in key areas would help. That would probably involve finding a way to keep Referendum going longer.
-Earlier election debates would also raise the Lib Dem profile, but since the elections in this TL would be even less close than OTL, there is not much of a motivation for a PM to participate in them. Maybe a Tory opposition leader agrees to do one without Blair to show him up, and the move backfires as Kennedy comprehensively beats them. Still, that would take a mildly stupid move on the part of the Tories.
On top of those factors, you could have Blair managing to get AV past the cabinet when he was doing constitutional reform. The preference votes are just enough to boost the Lib Dems over a Tory Party in chaos, and they become the official opposition, albeit a distant one.