You need to establish why its becoming waterlogged - causes could be, the lawn is lower than the surrounding area/s, so some sort of drainage should be put in, or there's something under the lawn which blocks drainage for a while, such as hard surfacing and so on, which might be possible to remove. If you don't establish what the cause is and rectify it, you'll just be swapping a waterlogged lawn for a waterlogged area of gravel.

Just a thought - if you are in a situation where you get leaves falling onto the area you may find it a total pain trying to collect them from gravel. Also be very sure you prefer a desert look to a green lawn as it would be a hard task to rectify it if you change your mind.