Decision tree lower bound for finding two array elements summing to zero
You're right that there are only $\binom{n}{2}$ many inequivalent solutions. Fortunately, $\Omega(\log \binom{n}{2}) = \Omega(\log n)$, so there isn't much difference between $\binom{n}{2}$ and $n^2$, in this regard.

However, this is a pretty bad lower bound. You haven't specified which queries are allowed, but assuming you're allowed to compute signs of constant degree polynomials, then I would expect an $\Omega(n\log n)$ lower bound, since the similar problem Element Distinctness has such a lower bound. This also matches the upper bound obtained by sorting (assuming your model supports this).

Indeed, this is just 2SUM (a sibling of the more famous 3SUM problem), and an $\Omega(n\log n)$ lower bound was proved by Chan, Gasarch and Kruskal in their paper Refined Upper and Lower Bounds for 2-SUM.