I am going to fake going on a trip to avoid being forced to work on my day off.
Why don't you want to go into work?
It's not that I don't want to work, it's just that I didn't want to put in a lot of effort on my day off.
I can see why you would say that. It's understandable to not want to go into work on your day off. You should just tell your employer no instead of lying, though.
I have a habit of lying when it's convenient.
That's a good habit to try and break, it can cause problems. For now, just tell the truth. It IS your day off, after all.