I don't know about the physical size but looking at the [guide|20485|LG G2 user teardown] and the [guide|19016|Nexus 5 featured teardown]:
* Nexus 5 battery reference is BL-T9
* LG G2 battery reference is BL-T7
* mAh's are different
* Finally the battery connectors looks not at the same places
I think we can conclude that you can't install a G2 battery on a Nexus 5, sorry. However, there is Nexus 5 batteries available on internet. Look for "LG BL-T9" on google and don't miss the [guide|26009|Nexus 5 Battery Replacement guide] on iFixit.