Was wondering if anyone knows, how much rain is needed for a fire ban to be lifted?

[EDIT: Sorry, thought I was in the Quetico forum. The below answer applies to Quetico - not sure it's the same for BWCA]

Per the ranger at Cache Bay, you can't go by rain totals at any given area of the park because fire bans apply to the park as a whole even if only a section is high fire danger. For example the current fire ban commenced a day after southeast Quetico had gotten over 1" of rain. But the northwest area of the park was super dry and hadn't seen any.

Because of this, while you are in the park, you can never assume that a fire ban has been lifted even if it's poured rain every day of your trip, unless you receive official word somehow.

Tough to answer. The rain has to be widespread over the whole affected area. It has to be enough rain and a slow enough, soaking rain to get deep into the soil, not just run off quickly. So many variables.