I am in a different time zone so don't know when 7am is. We use +2 or +3 etc after the shot as we are all in different time zones.
If you are not going to be home to test, I don't think I would shoot the full amount.
You could give what we call a big chicken shot, ie a smaller dose. Maybe 1 unit? What do you feel comfortable with?
I would also leave plenty of food out for him to snack on while you are at work.
For the future, it would be very helpful if you could get some mid cycle tests and some tests in the evening as cats usually drop lower at night. Lantus is dosed on the nadir not the preshot.