As mentioned, Catan is an example of a game that makes significant use of mechanical randomizers - yet more skilled players will have a pretty large winrate against new players such that there is clearly a meaningful decision space affecting the outcome of the game between players of disparate skill. But it seems that the root of her issue is lack of a meaningful decision space such that her decisions actually matter. I would say the best measure of a 'low luck' game is how often a more skilled/experienced player wins. On the other hand, I also vastly prefer games with very little type 1 luck (mechanical randomizers like dice and shuffled desks). This article sums up my thoughts on luck, and why every game not feasibly solvable in a humans head involves 'luck'.

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Games that only require luck