If I lived in East Lansing but worked in Lansing do I file city taxes for East Lansing as a resident and Lansing as a nonresident?

Yes, that's correct. As an East Lansing resident, you pay 1% on all of your income.

 

Since you work in Lansing, you pay 1/2% nonresident tax on the money you earned in Lansing. Follow this link for more details. 

You may want to check with the city before doing that.  I think, but don't know for sure, that it works the same in Michigan as it does in Ohio.

 

You do not have to file a city return for the city you work in.  You only file for the city you live in.  The city you live in may (usually) give you a credit for some of the tax withheld for the workplace city. 

 

You would only file a workplace city return if there was an error, in the amount of withholding and that's unusual.