Both lift and leverage measure the relation between the probability of a given rule to occur (support(A→C)) and its expected probability if the items were independent (coverage(A)*coverage(C)) of each other. The only difference is that lift computes the ratio of both factors (support(A→C)/(coverage(A)*coverage(C))) and leverage computes the difference (support(A→C)-(coverage(A)*coverage(C))). The implications are that lift may find very strong associations for less frequent items, while leverage tends to prioritize items with higher frequencies/support in the dataset.
You can get a broader explanation of all association rules and their formulas in this document.