Will water vapour travel through lime and feed mould?
When you say &quot;lime&quot; I assume that you mean some sort of mortar or plaster.
I see the brick or stone in the wall and some kind of material that has been troweled in around the drain pipe.
To answer your questions :

Gasses could move through unsealed mortar very slowly, but mold spores would not.

Water vapor would not travel through the mortar by osmosis, but it could wick standing water farther up into the wall. Seal the patch if it does.

If you don't introduce moisture through your patch, there's no problem with it being the most permeable spot in your wall. A mortar based patch is probably ideal.