It would be better if you provide the link with the exact article.
Not native speaker but I think it is:

Lits (autorisés) au permis

and it means the number of beds that a hospital (or another sanitary establishment) is authorized to have.

So

% de résidents sur le nombre de lits au permis

is the ratio of citizens over this particular number (counting several hospitals of a town for instance).

See here for example:

https://m02.pub.msss.rtss.qc.ca/M02SommLitsPlacesProv.asp

PS I add here Greg’s useful comment:

I concur with that, it is also the definition I have found here

LITS AU PERMIS : correspond au nombre de lits alloués par le ministère de la Santé et des Services sociaux.

Note that it seems to be a Quebec administrative term, if you look up the term on Google, all results are links to Canadian websites (as a Belgian speaker, I also had the feeling this should be the meaning, but I had never heard or read it before).