Is it ok to stack LPs horizontally?

Keep them upright to prevent warping.  Angled storage will eventually lead to warping as will laying flat due to the weight of other albums on top. Safe to lay flat, I suppose, if you only had 2-3 in each stack, but you would either need a very large storage area or a very small LP collection lol

I see a lot of LP collections with the records leaning to one side. As @dseltz just said, given enough time LP’s thus stored can become "dish" warped.

I years ago came up with a solution: you know the cardboard "spacers" you routinely find inside the mailing cartons your LP shipments arrive in? Don’t toss ’em, keep ’em and use them to take up the empty space in each section of your LP shelves. Doing so keeps the LP’s perfectly vertical, and one spacer can be removed for every new LP that needs to go in that section.

Record stores receive one or two spacers in each carton of LP’s they are shipped; ask your LRS for the ones they routinely recycle. I have two linear feet of them!

So you unstack a pile of discs just so you can play one, stacked one third way up. I have thousands of LP's all stacked vertically some dating from the sixties, not one of them warped !!!

OP has 'run out of storage space'.

So why does piling records horizontally occupy less space than vertically?  The records have a fixed volume.

And yes, horizontally will cause warping after a while.  Gravity will act on the less well supported outer areas and cause them to fall.

LPs should not be so loosely stacked that they lean to one side, weighing against each other.  Nor should they be tight enough to create side pressure.  Just densely enough so that the stand vertically without pressuring each other.

What you might try is go on Etsy and search for "vinyl storage". Perhaps a small footprint rack like the one below would be a solution.