Lantus does not last a full 24 hour in kitties. In humans and dogs it can with some. but not with kitties, since their metabolism is much higher.
Are you testing glucose at home? If Whiskers has been having lower numbers it would be good to be able to get tests at least before shots and at midcycle to make sure he is not going too low. If he needs to drop the dose from 1 unit a suggestion might be to give 1/2 unit twice a day at 12 hour intervals if you are home testing