I'm surprised that I worked right through my lunch break.
Did you have a compelling reason for not eating lunch?
I had an important meeting with a client that I had to prepare for.
I know that you needed time to get ready for your client, but missing your lunch because of it will drain out your energy. Going to your meeting on an empty stomach keeps you from being able to concentrate fully.
Yeah, that's what happened. Now I feel burnt out.
That sucks, but it can be a good lesson for you not to skip lunch in the future. Skipping lunch in favor of work can seem like a good idea in the moment, but it can negatively impact your work down the line.