Do I have to use sucrose to induce a lac promoter?
You can induce the lac operon by two things: Lactose (or more precisely Allolactose a metabolite of it) and lactose analogons which are not metabolized by the bacteria. 

Lactose induces the expression and is metabolized while IPTG is not a target of the $\beta$-Galactosidase and will give you a strong and permanent induction. Sucrose will not have any effect on the promoter.