I think you are totally doing the right thing by keeping on taking the lantus down... if you are regularly waking at a low level and regularly going low at tea time, that really sounds like the lantus causing the problem to me. Especially as you are saying you don't even need novorapid at meals... that sounds like your lantus is way too high for you. I know everyone's different but just for comparison, my lantus levels are 16.
As for treating hypos when you aren't hungry, I used to force loads of food down me when I was dropping low, but actually I've found that just a gulp of sweet drink or two/three wine gums can often lift me out of it, especially if it's 4ish rather than lower. A relief, because it is horrible trying to eat when you don't want to. Every hypo is different of course. Getting the lantus to the right level will be the key.