I Was Late For Work With No Excuse And Was Fired And Now I Want To Sue

I was recently terminated from my job because I was late. I did not give an excuse or a reason for my lateness. I called before my shift was scheduled to alert a manager of my lateness & nobody picked up, so I call at the exact time I was supposed to be there to alert someone of my lateness. After ringing for a while, the General Manager picks up the phone jokes around with me after I tell him I'd be 15-20 minutes late & asked if it was alright to still come in. I walked in ready to work 20 minutes late as discussed, as soon I began to work he pulled me into the office to fire me for being late. I refused to sign our writeup explaining why he fired me because I didn't agree to any of it &I had the chance to write on it what I felt but I was so angry.
Is there anything I can do?
Is that legal, or right?