I found the 30m Aster DEM for St Lucia, but am wondering if there is some DEM or other elevation data source (Lidar) with a higher resolution. I googled, but have been unsuccessful in finding any free data source.
I've done some environmental consultation on that area and the best available resolution for a DEM there is probably the ASTER GDEM 30m. Even then, that data isn't processed/cleaned so you might run into problems with clouds/reflective surfaces giving you false values.
The thing with Lidar is that it costs quite a bit of money to produce and while some places may release this data through an open license, coverages for most other places (especially true for the Eastern Caribbean) probably rely on private/public partnerships and as such, can't afford to release this data for free.
One repository I use is EarthEnv 90m (http://www.earthenv.org/) as it integrates SRTM and ASTER to give continuous, error-removed surfaces.