Well any water based lube will just wash away in a pool, so that honestly won't work at all. I'd suggest using a condom to cover the dildo (perhaps completely covering the base as well) and then using a silicone lube (personally I'd suggest Pink or Eros). If your silicone dildo is very high quality (Tantus for example) it may be worth doing a very small spot test on the base of the dildo with some silicone lube to see if it reacts (I've had very good luck with Eros lube and Tantus dildos). If it starts getting gummy then you need to scrape it off, but if it stays slick then you are good to go.

Since you're in a pool, the lube that's on the dildo won't be really hanging out and melting the dildo - you know what I mean? It'll be getting smeared around or floating away into the water. I'd be willing to bet a dildo that using silicone lube will be just fine, especially since a lot of popular silicone dildos are high quality silicone and will be fine with silicone lube anyways. Also, have her pre lube instead of pre-lubing the dildo - that way the dildo's not sitting with silicone lube on it

Have fun!
Probably best to do the inital penetration out of water, to avoid getting irritating chlorine inside. Used the steps