Translation:That warrior always defends his home and he is willing not to travel.
It's a weird sentence in its limited context and keeps attracting the "Correct solution is unnatural and has an error" comment. I think it should stay, though, because it forces students to read/listen to what is actually there and not just arrange the components --travel, willing, not-- into the the expected answer. We can endure some complaints in return for others learning.
That is not "the natural way to say it" in English; it is a natural way to say something else.
lengbe'qang is "he is willing not to travel" or "he is willing to not travel" -- if you tell him to travel, that's fine, but if you tell him not to travel, that's also fine, because he is willing to stay at home and not travel. He is willing to (-qang) not travel (lengbe').
lengqangbe' would be "he is not willing to travel" -- if you tell him to travel, he will refuse, because he is not willing to do so. He only wants to stay at home. He is not willing to (-qangbe') travel (leng), or to put it differently, he is not (-be') willing to travel (lengqang).
The suffix -be' is a rover -- it can "move around" and appear in various positions in the list of suffixes on a verb. It negates the thing which is right before it -- whether that is the verb itself or some other suffix.
So when there's a -be', you have to pay attention to the position in the list of suffixes to see what is being negated.
I came here because although I was marked right for "he is willing to not travel", it said that another solution is "he is not willing to travel". I thought "he is not willing to travel" would be "lengqanqbe'", not "lengbe'qang". I saw this comment of yours seemingly indicating that I'm correct about that, so it seems like Duolingo is accepting an incorrect answer for this.
it said that another solution is "he is not willing to travel".
I can't find any sentence with "not" before "willing" in the list of accepted alternatives. Did you happen to take a screenshot?
What there is is variations on "he is willing not to travel", which is what some conservative English speakers prefer in order to avoid the (arbitrary) prohibition on "splitting the infinitive".