During the medieval period and renaissance, could a medieval merchant or group of merchants, a company or corporation if they were called that back then, buy or rent land from foreign entities, say a king or lord, for commercial purposes e.g. to grow cash crops on. What that possible in those times, if so how?
Not really in the way you are thinking. The socio-economic structure of medieval Europe would not have really made such a proposition feasible, and frankly, I think most local lords would have been skeptical of such an arrangement. I'm not sure how this could benefit them more than individual peasants farming their lands. What you see more of is merchant companies (compagne in Italian) looking to get what are essentially enclaves or even whole settlements where they could conduct business. The Genoese colonies at Galata and Caffa are excellent examples of this: zones of cities where they could hold sway and organize business operations. According to Steven Epstein, they even tried to get a small town on the west coast of England, but the king refused.
Now, I know for a fact that families could own lands outright and incorporate them into their business arrangements. Specifically the Bardi company in Florence owned lands and Tuscany and had a network of mills where they processed wool to be dyed, spun, etc in the city itself.