Harnessing phase separation to easily make Li film
You are thinking in the wrong direction. Meniscus is not about pressure at all.

You seem to be imagining external hydrostatic pressure as a huge invisible flat lid that we put on top of your molten lithium and kinda force it to stay flat. This is very much not so. The pressure is the same all around, thanks to the Pascal's law. It does not affect the shape. It presses on the curved sides of the meniscus with the same force as it does on top. The very notion of "flat" is simply not there.

If anything, it is gravity force that reduces the meniscus. In effect, adding a liquid on top will partially negate the gravity and thus make things worse. Keep in mind that such liquid, if it is found (I still can't think of any, and I'm not a novice in chemistry, mind you) can't be much less dense than lithium, which almost brings us to the conditions of Plateau's oil drop experiment, with lithium playing the role of oil. Not quite the outcome you wanted, is it?

It is the surface tension that matters, and adding liquid might change that in an unpredictable way. Then again, you can achieve the same result without any extra liquid. Just use different material for the container. I guess using metal instead of glass would make the meniscus bend in the opposite direction. With some tweaking, it might be possible to find the material with wetting angle of $90^\circ$ that would make lithium surface perfectly flat, but I don't think it is worth the effort.

So it goes.