I can only relay what I do, and it may be something nobody else does. When I DO play slide on anything, lap or strapped on guitar, I use open D. I would rather tune strings down than up, but that is more of a consideration about stressing the neck tension by tuning up. Especially on that 3rd string. Because it's a thicker string that move from G to G# always made me nervous. Same logic for D to E on the 4th.

But open D, tune 1 down to D, 2 down to A, G down to F#, 4 and 5 don't change and 6 down to D. All down. And in that kind of band I also had one on stage tuned in open G, from top down D, B, G, D, B, G, but the string on the 5th string was a thick D string rather than an A, and the string on the 6th string was an A rather than an E, so again, all the detunes were down. The only drawback there was that when I had to change to that guitar the front man had talk to the crowd because it always required tuning from song to song. If I used the open G early in the second set and needed it again late in the second set, it was badly out of tune by that second use.

Lap guitars are meant to be played with a slide though, and the construction is probably completely different. I know they are much beefier than a standard guitar. Never had one so I don't really know. I have played a lap steel I borrowed but never owned one.

I might buy a pedal steel. They have always intrigued me. Knee lever this, pedal that, volume swells... Sho-Bud, Fender, whatever. Just to learn how to play it.