Well you could, but I wouldn't recommend it - Lavender likes light, free draining soil in a full sun situation and is relatively drought resistant - Fuchsia likes a little shade from hot sun in the middle of the day and does better in a richer soil that's watered regularly, as does Begonia. Lavender also is a permanent, woody shrub which makes a sizeable, rounded bush, and will rapidly cover the surface area of a pot with its foliage and stems.

Not sure whether you mean Bergenia or Begonia?
If you mean Begonia there are two kinds, the little sempervirens which are grown as annuals in the UK, or the larger ones that grow from corms and need overwintering frost free. These make large plants and to put them with a Fuchsia you would need a pretty large pot.

I would put the fuchsia in a pot on its own. If it is a tender one it will need to be taken into shelter in the winter and if it is a trailing one it will take up the whole pot by late July. If you have the label we could probably tell whether its hardy or not.