The Google Nexus 5 is always sold unlocked, so yes it will work on Koodo. If you mean by "support" does Koodo sell it, no :( Only the 16GB version I'm afraid.
I don't think the SIM card of your LG500 will work, I believe that is a normal size SIM card? True? And the N5 has a microSIM. However you can just purchase a SIM from Koodo and activate that in your self service :)