Doubt in the correctness of decision tree models for constructing a lower bound
The bound you're describing is that the depth of the decision tree is at least the logarithm of the number of distinct answers. This bound always holds, but is not always tight. In the case of searching an element in a list, it is tight when the list is sorted, and not tight if we don't assume anything on the list. The reason for this discrepancy is that the bound doesn't distinguish between the two cases &mdash; it is too general.

I challenge you to come up with another argument showing that the depth of a decision tree for finding an element in a list is at least $n$ (or even $n+1$, depending on how depth is defined).