Since 1990's or 1980's all multi-family housing must be ADA compliant. FHA also has laws/rules on disability requirements.
https://www.hud.gov/program_offices/...accessibilityR
https://adatile.com/do-apartments-ha...ada-compliant/
Thus any new construction for these "lottery" buildings regardless whether or not they offered "affordable" or "low income" housing would have to meet requirements above.
Most of those requirements speak to accessibility of building, common areas, and some other bits like ground floor units.
What ADA and other laws do not speak to is individual units being in compliance with said laws.
https://www.realpage.com/blog/3-misc...sibility-laws/
This means largely ensuring doorways are wide enough for wheel chair access and some other small bit, apartments are not required to be modified in order to suit a specific disability. If a developer wishes to create such units or whatever on their own or with a carrot/stick from city, that is another matter.
What said preference for households with verified disability does is basically carve out unit or units that will be set aside for a "special" group who often have issues finding housing, especially something they can afford.