How to generate Latin HyperCube Samples for a triangle?

I need to populate a specific triangle with exact number of random samples of equal distance from each other. If this was a square, I'd use Latin HyperCube Sampling method. The problem is I need the number of samples to be exact, so simply generating samples for a square, and then discarding all the samples not in the triangle does not work. Any ideas are appreciated!

p.s. I'm using LHS library in R.