Scotland has a deer problem (they have no natural enemies anymore). So any reforestation effort fails because deer eat the shoots and young trees (just look up the Brewdog reforestation fiasco). The re-introduction of a predator would bring balance. Wolves would do, but people and especially sheep farmers are very scared to do that. The lynx is a less intimidating option.
I’m not from Scotland, but I live in Belgium, where wolves are making a comeback, even in Flanders, and lynx are also back in the ardennes. I’d say Scotland has A LOT more wild land than Belgium, which is massively paved over and farmed intensively.
I don’t think it would take on an adult red deer. But roe deer definitely, and probably fallow deer too. They are known to hunt animals well above their own size. And sure, hares and smaller animals too.