David Lammy is a race-baiting racist who sees the whole world in terms of race because he's a racist. He's the go-to rent a racist for the Guardian and the BBC because he's guaranteed to have some stupid racism to spew on any topic, guaranteeing some good clickbait.
The campaign in question won't work because slogans don't work, but it's got nothing to do with race. If however you want to get hashtag slogan takeaway boxes into the hands of young people in the UK, chicken shops are the places to use. "The kids" buy boxes of peri peri chicken, not fish and chips, burgers or organic salad. That has nothing to do with race. There is absolutely no racial connotation in the UK in buying chicken or even watermelon. This isn't the USA. But David Lammy is a racist, so he'll see race in everything.
Having spent several years married to an Indian in the UK, I've always found it both instructive and prudent, when a member of a minority group tells me that she or he considers something racist, to listen to what's being said and to take it on board, since I'm not the one experiencing what the other person sees as being based on harmful stereotypes.
Simply telling them they've got it wrong and they're being oversensitive or racist themselves or whatever always seems to me a bit like a man responding to a women telling him she finds something he's going or saying sexist or demeaning by saying, "Well, actually, it isn't anything of the sort because..." which never ends well, at least in my experience.
This has always been pretty much second nature to me, since I'm of an age and background to have been brought up on the principle that should someone take personal offence at something I've said, then unless I'm actually trying to rile the other person, I should apologise and make a mental note of what has been said and consider the implications, since a lady or gentleman should never unintentionally cause offence, at least not if they're English.