“to train with ~”
It is true that many activities that use dumbbells are not strictly “lifting”, so if you want to be more general, and say simply that you are using dumbbells in a variety of physical activities, you can say:
- I train with dumbbells
- I work out with dumbbells
The verbs here are “to train”, and “to work out”.
- to train (v): 26. undertake a course of exercise and diet in order to reach or maintain a high level of physical fitness.
- to work out (v) to exercise in order to improve the strength or appearance of your body
Both of these are intransitive (i.e., they take no object).
But, if you want a transitive verb, then the best verb is indeed “to lift”
In English, the activity of using weights for muscle training is most commonly known as weightlifting, or sometimes just “lifting weights”. As a result, if you say “I lift dumbbells”, people will understand your meaning.
Avoid specialized terms for general writing
Within the fitness world, the act of lifting and lowering a weight to build muscle could be called “pressing” (raising up and down) or “curling” (bending at the elbow), depending on how you are using the weight, but I would not recommend these words because they are specialist terms, and would not be widely known to people who are not interested in weight-training. (Particularly “to press” is a verb which has many other meanings in English)