It's not a safeguarding issue to not be able to account for a child being in the dinner hall. At five they will be pretty much herded in there but no register will be taken.
If she's not eating what's on offer and you are worried then send a pack lunch. They will encourage her to choose something and eat but they won't force feed her. From experience staff are around and most often sit with the littlest ones.
In regards to lying it's not so much that they lie but my teen works with five year olds and they make up brilliant stories about not being fed, being in the pub, having a pet unicorn, climbing over a rainbow etc. They will swear they haven't been or done something or had their turn or their cake when you know they have.
They will choose to go to the wrong place because little Chloe who is their best friend goes there and then claim it wasn't their mistake.
Mine told me the teacher had said I was crazy at that age...
Seriously have a word with the teacher. Tell them you paid for club x and she's going to club y.
Tell them you are worried she isn't eating and can they keep an eye on it.
You might find she's choosing to go to yoga because her friend does or something.