I used to lie to people and tell them my dad was dead because it was less awkward than having to explain to them that he abandoned me
I gotcha. So what was the reason you wanted to lie about it?
I was embarrassed about it
I'm sorry that happened to you!  A parent should never abandon their child like that.  It's perfectly understandable that you'd want to keep that private, but you definitely shouldn't feel embarrassed about it.
I'm doing fine, I went to therapy and I'm doing well. Thanks for being concerned.
You have a right to only share the details that you feel comfortable with. I do hope you have someone you can talk to.