Hi Sue,
Right around the lake itself there are only small clinics and doctors office. If you are close to the volcano side of the lake there is a public hospital in Ciudad Quesada about an hour away. If you’re where most expats are, further north/west on the lake, there is a clinic in Nuevo Arenal, a larger one in Tilaran, and then another hospital in Canas. Those last two well off the lake shore, so a bit of a drive. For major issues or specialist care you’d probably go to Liberia, about two hours from Arenal. Or to San Jose, about three hours away.