This argument is likely to be Labour's official line over the next 6 weeks, but its a flawed argument designed to make Labour seem like the best choice for Remainers.
The line of reasoning supposes there's only one way for the Lib Dems to have any influence, which is if they're in Government. That's plainly false. If the Lib Dems have a really good election, say 40+ seats, then they'll return to Parliament able to have a significant impact on proceedings. With that number of MPs, Labour would more than likely have to work alongside the Lib Dems, and more pertinently, it would make it clear to Labour a clear Remain position is preferred by many Remain voters than the position that Labour has taken.
In 2017 Labour's performance in the election was seen as an endorsement of their pro-leave position, even though many Remainers voted Labour, and it opened the door for Labour to continue to avoid backing Remain over the last two years. The worry for me as a Remainer is that a vote for Labour now will be seen as a further endorsement of their current position, which is at best "TBC", and at worst, they won't back Remain in a second referendum but will stay neutral, which I personally think would be bad for the Remain campaign.
If the Lib Dems have a strong election, then I think that pushes Labour into an overt Remain position as well, which I think is good if Remain is what you're after.
Which isn't to say that you should automatically vote Lib Dem if you want Remain. A good Lib Dem campaign probably equals a bad Labour campaign, which risks the "Vote Lib Dem, get Tories" proposition, that's not a small concern. And of course in some places the Lib Dems just aren't a force and its a simple choice between Labour and the Tories anyway. But the argument being made is only half the story.