They probably have sugar in them, but if you're ill, you're ill and that must come first. You shouldn't skip meals or cut back just because you're worried what a lemsip might or might not have in it!
If you want to be sure, just take paracetamol tablets and drink a cup of hot water with a little honey and lemon juice (you can then measure the syns). If you're needing the caffeine or decongestant that lemsip-type products contain, get some 'cold and flu' capsules and stick with the hot water!
Hope you get well soon!