@Wesley Wong the exit clauses are case by case. The duplex that I rent has this exact clause but others don't. Some landlords want to control the timing of vacancies in their rentals so they are strict. Others haven't even thought about it. Like everything, rental leases are negotiable contracts but the more desirable the place the more likely the landlord will get their terms. You might probe your landlord to find out what is most important to them then give them what they want so you can get what you want.
Have you checked to see if your landlord wants to sell your current place to you? If they own it free and clear you could do seller financing then use your loan to buy a rental.
Another option is the foreclosure auction. My brokerage (Caliber Real Estate) specializes in buying at the foreclosure auction using hard money and in your case refinancing after acquisition. This is a big week at the King County auction. Let me know if you want more info on this and we can talk about the details.