So I have a multisite with the main site

So I have a multisite with the main site (nutritionbyaleks.com) working fine and a subsite, using a subdomian (fit.nutritionbyaleks.com), which also works fine.

When I try to map the subsite to a different domain (firstirontri.com) it tells me "Domain name is unavailable to access". The domain has been registered for some time and is set as a parked domain through a different registrar (the WP install and domain names are on different servers).

Both domain DNS settings are pointing to the server where WP resides.

I'm wondering if a dedicated IP is required for this situation. If not, please help me find the problem.