LOT is a Euro carrier and your journey commences in Europe. European law should apply, although I am no longer sure of what that is with the very recent Passengers Bill of Rights (or similar) coming into effect in Europe very recently. I would try to track down a copy of that on the www somewhere, as I believe it heavily favours the passengers rather than the airlines in many respects, from what I've heard about it.
Then again, you haven't stated where your travel is commencing from, so if the starting point is a place that isn't a member state of the EU, then that's not going to be any good to you I would imagine.

Your travel insurance should also cover much of the extra expense, pending the type of cover your purchased, or at least be of some assistance to you.