I was locked out of my home business and paid a locksmith $113 to get in. Can I claim that expense on my taxes on either Office Expenses or Home Business Expenses?

It depends.  If you were just locked out of your home in general then you could include this as an expense for the entire home that would be deducted on a prorated basis for your home office.

If you were locked out of your office itself, then it would be fully included in the home office deduction expenses if you are taking the actual expense method instead of the simplified method.