pH level of fabric with regard to inhibiting fungal growth
Hypochlorite bleach is a potent biocide, so throughly washing clothes with it should kill all fungi. The pH part is true, bleach is alkaline, but so are all common detergents. But this should not even matter, if the clothes are properly rinsed with clean water, that should remove almost all of the bleach and restore the pH to close to neutral.
What I think happened, is that his clothes were not rinsed well enough, so traces of the bleach and the detergents stayed in the clothes, causing or exacerbating skin problems. Some people have skin especially sensitive to bleach and allergic reactions to detergents can happen to.
So I would recommend washing with bleach, but making sure the clothes are well rinsed. You may need to set your washing machine on an extra rinse cycle to get the desired effect. Using lemon juice should not be necessary.