You didn't say how you found out you will be losing your job - were there some rumours (which may be totally untrue) or did your manager or HR or someone else who would know tell you officially?
In the first case you would first make sure that this is actually true. Often people make assumptions that turn out to be wrong.
In the second case, any manager ...
First, don't lie to your boss by telling him that you have:
a doctors appointment
you need to attend to a funeral
that your dog needs to to see a vet
or anything similar..
A lie is not just a personal burden for anyone with at least a bit of conscience, it might also eventually be revealed. Besides that, your boss might do the math after finding out that ...
I have an appointment to go to for personal reasons. You can say 'doctor appointment' but then you run the risk of them asking for a doctor note which you won't be able to provide and that can get you in a jam. People have to go do stuff all the time, you don't need to give your life story. People around you are probably doing this right now.