The center of a converging lens is generally thicker than its rim.
The center of a diverging lens is generally thinner than its rim.
There are exceptions regarding meniscus lenses
Examples for converging lenses:
All convex-plano lenses, all plano-convex-lenses, alle biconvex lenses …
… as well as all meniscus lenses with identical radiuses :
Examples for diverging lenses:
All concave-plano lenses, all plano-concave lenses, all biconcave lenses