I have just tried the Gountlet. The mission that's seem to be too hard, meaning it's not that likely that they could easily kill your lord, only you need to play it patiently. I fed my people with cheese and meat, and I was cutting wood and producing weapons with several workshops.
Right now another idea came to me - there is so much wood so I could produce spears and sell it. This would bring me enough money for later attacks. Some time later I should be able to build hops farms and to produce bear, thus to earn some more gold with inns.
After that - you need more patience in destroying enemy walls. For that I may suggest you to consider not just using of catapults but using rams and siege towers as well. If you need any specific help about any of those three missions feel free to ask. That would be easier than telling every tiny detail.