I'm going to pretend to have a lot of work to do so that I can stay late and spend time with a co-worker
Why is your reason for trying to stay late with this person?
A lot of things are happening in my life at this point in time
It's good to want to try to spend time with someone you are interested in, but you should not withhold truth about having a lot of work to do. Good relationships are based on honesty.
It's not a lie, I'm actually working on a lot of stuff. Don't judge me.
If you are staying late to do your own work, that's great. If you are staying late in the hopes that you will get the other persons attention, just understand that they may not want to start anything at work. Ask them to hang out after work some day!