Since she's on the lease and we still have to pay until December, is there any action I can take to get her to pay the remaining half of the lease?

The affair is irrelevant under Nevada law as we are a no fault state. The lease debt is a community obligation. You can file for divorce and ask that she be assigned half that debt. However, generally people are required to pay only their own living expenses, and there is a lot more analysis involved such as each party's income, the length of the marriage, and other assets and debts. If the lease is ultimately broken, that also becomes a community debt to be dealt with in the divorce. You need to consult with an attorney to go over your entire situation to determine what options you have and how best to proceed.