Generally avoid putting stress on the area is important in trying to heal fractures.
Usually for any break in the bone itself -- a healing period of 3 months is generally used. 3 months is usually the minimum, and can be up to about 6 months.
Without actually knowing the degree of the fracture (mild, tiny, large, etc) it is impossible for anyone on the Internet to advise you to the appropriateness of the activities that she can engage in, though both the speed walking in the pool and gentle swimming should not put that much stress on the L5 body. Activities that would cause her to bounce up and down (running, basketball), or put stress on the back (leg squats, sit ups) -- are definitely out.
And if her doctor told her 3 months -- 3 months it is.