Well outspeeding it is an option. Locking it down is another. Vilegar should have a favourable match-up if only because Lostgar would simply lose all its VS Seekers. Deafen lock is a sure win, of course.
There's also Looker's Investigation, Cyrus' Initiative, Judge, etc., all cards designed to stop them from playing the Stadium. Cyrus' Initiative would be most effective, but expediency Looker's would be more beneficial for other matchups.
And if all else fails, you could simply not put down basics...and shuffle them all into your deck. Since Lostgar's damage is essentially zero, what can they do against, for example, a lone Tyranitar with Expert Belt?
Either way, it's time for people to use a lot more Looker's Investigation at least.