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