Yes. There are LED fixtures for use in or under water. IP rated fixtures are expensive, I would think that for what you are describing even renting them would be over the budget.
You could use LED novelties. There are all kinds of globes and other floating LED novelties that would be much cheaper than trying to up light water.
You could also light the pool from above using framing spots and breakup patterns. This would be attactive without disrupting the pool itself. (I'm not sure if the intention is to introduce the new pool that they will agree to distorting it's true appearance with LED fixtures underwater.)