You can either use an expression which connects both columns as base for categorised style, or you can go for rule based styling. As to the specific formula: Either you give some more and clearer details on your data structure and the intended display, or you work it out yourself based on the examples in the expression dialogue.
/edit: Okay, it really is quite easy: Go to the style-tab, choose categorised and enter the following:
if ("use"='street',"lamp_type","use")
Basically this says: If the feature is registered as a street, categorise it based on the column "lamp_type", else use the column "use".
Have fun fiddling with your symbols, and bear in mind: Best not use more than seven colours, and ideally use the same colour for all "street"-features and differentiate them by using different strokes.