How to waterproof our existing "lower ground" floor
The only effective way to waterproof a masonry wall is from the outside - so if your alternatives are to coat the inside of it or run the water elsewhere, run the water elsewhere, as coating the inside is doomed to failure.

If the coating is on the exterior and the water is trying to get in, the water pressure holds the coating in place. If the coating is on the inside, the water pressure will pop it off, sooner or later. If the waterproofing was not put in place as the wall was built, on the dirt-facing side, it's probably never going to work - or it won't work for long.