I don't actually know. But essentially anywhere with a large amount of open ocean on it's coastline will get swell. Then it's a case of - are there any places the waves will break well. I'd guess that St Lucia has beaches so will have beach breaks at least.
On magic seaweed there is this:
http://magicseaweed.com/Windward-Island ... recast/40/ which I think covers that strech of islands, St Lucia isn't mentioned explicitly though.
edit: just remembered, the main reason it might not get waves is if it has extensive offshore reefs. The swell will then break on these and not get through to the main island.