The post Coherent decisions imply consistent utilities demonstrates some situations in which an agent that isn't acting as if it is maximizing a real-valued utility function over lotteries is dominated by one that does, and promised that this applies in general.

However, one intuitively plausible way to make decisions that doesn't involve a real-valued utility and that the arguments in the post don't seem to rule out is to have lexicographic preferences; say, each lottery has payoffs represented as a sequence and you compare them by first comparing , and if an only if their s are the same compare , and so on, with probabilities multiplying through by each and payoffs being added element-wise. The VNM axioms exclude this by requiring continuity, with a payoff evaluated like this violating it because but there is no probability for which a probability of a payoff and a probability of a payoff is as exactly as good as a certainty of a payoff.

Are there coherence theorems that exclude lexicographic preferences like this also?

Why would you wait until t=1? It seems like at any time t the expected payoff will be (1−t2,0,…), which is strictly decreasing with t.