Usually, in the days after an election, the winner does all they can to maximize the claims of mandate. Here, you see the opposite, with the Boris Johnsons of the world basically denying everything. If I were a leave voter, I am no longer sure what I have voted for. So good campaigning is about getting a result without promising things for which you will be held to account.
The sins on the Remain campaign side are much worse. In a proper campaign, techniques of micro-targeting would have caused every interest group to know about the specific grants that would be lost, the road and infrastructure projects that would be abandoned, the jobs that would be at risk. Yes, even British plumbers would know of the risk — and British homeowners (particularly those who enter into home improvement contracts) would know of the likely increase of plumbing costs. (I know that UK election rules are different from the US, but right now, at least, its hard to argue that they are better!)
Moreover, the absence of vision in either campaign was astonishing.
So, this suggests that no-one is qualified to lead the battle to reverse the result. But is also suggests that a properly run campaign has every chance of winning, provided a way can be found to make it seem legitimate. The question is whether the Liberal Democrats can summon the energy to do it right. A least they have the legitimacy.
I would point out only this. At the time of the earlier referendum, there was no provision in the treaty for secession. So the will of the 1975 voter, for a final non-reversible judgement, is being thwarted by this vote. Anyway, if politicians are allowed to change their minds, why not voters?