When you updated, did you do a factory reset?
I know that OTAs are supposed to be able to upgrade... but going from KK to LP was a MAJOR upgrade and plenty of people are having issues with their phones that can be resolved by a simple factory reset. Unlike apps like facebook or gmail.... your camera app interfaces directly with the hardware layer on the phone. If something comes in a bit sideways, it can cause a kernel panic and your phone could reset as a result.
First... go in and clear the app settings for the phone (Settings - Apps - All - Camera)... if that doesn't work, you might have to go full out and do a factory reset.