The best thing with LT is its a total food replacement diet. If you follow it 'by the book' you'll lose weight very quickly. If you for whatever reason simply cannot stick to the diet then having small amounts of fish/chicken will keep you in ketosis, but obviously they have calorific value and thus you will not lose weight as quickly. I'm doing cambridge diet at the moment and they have a sole source + which basically includes a small meal which could be chicken or fish and certain salad leaves/veggies etc.
The problem with LT is if you do pick, it is very easy to fall off the wagon whereas if you just stick to ss then you don't even have to think about what you are eating.
I'm back on day 2 of ssing as I gained 10lbs back (2 is gone already), but I am ssing fully at the moment....no meals at all and I promise you, it is tough the second time around.