My husband is on chemo tablets for the rest of his life too. It is my understanding that this type of chemo only targets the cancer cells, not the healthy cells so the immune system is not compromised in the same way that "traditional" chemo does. However, my husband has been told to protect his skin from sun exposure as the tablets make his skin more sensitive so she should certainly speak to her oncologist for advice and written confirmation if it is ok to go ahead. (I'm thinking of curing gel under a lamp). - I have to say that his nails are absolutely fine though, not dry or brittle, so her nail condition may not have anything to do with the chemo tablets. They don't make you loose your hair either.
Just as a note, a terminal diagnosis is understandably devastating, but as we have found out, it doesn't mean it's imminent. My husband is 3.5 years into treatment and classed as in remission (despite being told his cancer was terminal/un-curable) and we know of plenty of others who are still going strong many years after diagnosis. Hopefully your client will be one of these and will therefore want to live her life as normally as possible - hence wanting to have her nails done. She just needs to make sure anything she has done is safe for her and not putting her at risk.