Pronouns
Let’s do our part, switch off your lights, the above exhorts.

It sounds strange for two reasons. For one, the first clause is in the first person plural (us, our) while the latter is in the second person (your) — so there is an abrupt and puzzling shift in perspective from inclusive (speaker + addressee) to exclusive (addressee) pronouns and determiners.

For another, without a context given, switch off your lights seems to suggest that the addressee has lights on him/her. (However, with context given, it would sound less odd, e.g. You forgot to switch off your lights when you left last night.)

The message might have read:

Let’s do our part; switch off the/all lights.