Ds1 was hopelessly disorganised when he started senior school, and within the first few weeks, he rang me several times asking me to drop off things he'd forgotten - he would meet me outside the office at breaktime. The last time I did this, the receptionist came out and sent ds1 off with a flea in his ear, telling him parents weren't allowed into the school willy nilly during the day. When he'd gone, she turned to me with a smile and said, 'I hope you didn't mind my saying that - it's not really a problem you being in school, but I am sure it's an extra hassle you don't need, to have to keep dropping off forgotten stuff at school - so hopefully now he will remember his things!'
Someone has asked why the receptionist in the OP 'kept on repeating that she'd do her best' - I would assume it is because the OP kept on and on at her about getting this lad's lunch to him and how important it was.
I do now usually take the view that if the dses forget something, they have to take the consequences. Ds1 is off to university next year, and I am not going to be there to fetch and carry stuff he has forgotten, so he does need to learn to take responsibility for his own stuff. If one of them forgets his lunch money or some homework, they go hungry or get a detention or punishment exercise - I am not gleeful about this, but consider it to be fair.
Perhaps the receptionist in the OP was stressed and let it spill over into her manner, which she shouldn't have done - but she is human, and I know that I have sometimes responded similarly when stressed - I suspect most people on this thread would say the same if they are being honest. I do suspect that the receptionist was polite until the OP carried on nagging her.
I have to say that I am utterly gobsmacked at the OP ringing the deputy head 'because that is what the staff are there for' - fgs the deputy head has plenty more important things on his/her plate than chastising the receptionist for not grabbing the lunch and hotfooting it round the school in search of little Johnny! 