You may ask a friend who has a lease to go with you. just tell them that you are now staying at your friend's apt. i think this should be ok. acturally when i was applying for the SIN, they even didn't ask me for the lease. just fill a form, show them my passport and visa (i'm holding a visitor visa as a temporary employmee). that's ok. For immigrant, i think maybe it's the same.
to hsif: They didn't ask you for it, because they don't ask anybody for it. Not nessesary at all!
sin card is for all the residents of canada, they don't care whether you have a lease or even a address.If you have landingpaper and passport, it's ok. wink