My party negotiated a truce with the Nothic in LMoP, then shortly afterwards the wizard found the sword hidden away and decided to try and steal it. The Nothic noticed and engaged in combat, at which point it was killed. In the guidebook, it mentions that the party gains 450 xp for killing or negotiating with the Nothic, but what if they did both?
XP are for overcoming an obstacle. No matter how you overcome it (sneak around, negotiation, killing), you get XP.
the wizard found the sword hidden away and decided to try and steal it. The Nothic noticed and engaged in combat,...
The obstacle is overcome only once in the description: because they failed in stealing the sword or negotiating for it, the obstacle had not been cleared yet, no XP were to be awarded as the Nothic was still an obstacle. Only the killing actually overcame the obstacle of the Nothic stopping them from getting the sword.
So the XP are only awarded for the killing.
Even if they had negotiated and then killed the Nothic, they would not have gotten the XP twice: that is an inclusive or, which means "(A) OR (B) OR (A&B)".
We can examine this with some basic logic. The last sentence of the encounter states:
Divide 450 XP equally among the characters if the party defeats the nothic or negotiates a truce with it.
We can parse this more precisely. Make the following definitions:
A: the party defeats the nothic
B: the party negotiates a truce with it
C: Award 450 XP
The statement quoted above is logically equivalent to:
If (A or B) then C.
From here it should be clear that even if A and B are true, we only award the XP one time.