The justification is that, if they win a majority in Parliament standing on that policy, they will have a mandate to revoke. However, they're comparing chalk and cheese. Typically, Westminster governments get around 42-45% of the popular vote: no party since the War has had more than 50%. The Lib Dems know this better than most, since they have used the fact to campaign for voting reform for decades. The referendum Leave vote, as we know, got 52%.
I think we've learned pretty thoroughly by now that Parliamentary democracy and democracy by direct plebiscite don't mix - but, partly for that very reason, having opened the Brexit worm can in one way, it can only be closed the same way. If I were a Leave voter, already resentful that my voice is ignored, having the referendum result discarded by fiat, by a Government with (as it would likely seem to me) less legitimacy, would make me feel that democracy had died altogether.
And that's a feeling that could very easily be exploited.