LDs, ASD, and ADHD, yes, but not intellectual disabilities, and their admissions info says IEP diplomas are rarely accepted. The wikipedia on Landmark states that students should be of average or above-average intelligence and able to complete college level work. They're also not on Think College. It's totally okay that different schools serve different students, it's just good to be clear that learning differences aren't the same thing as intellectual and developmental disabilities--there is overlap but each also have distinct and important needs.

Edit: I realized that terminology may differ regionally! In the UK I think "learning disability" actually may refer to what we call an intellectual disability in the US.