Can I have a friend, live at the condo without lease?

Obviously, the HOA is going to take the position that this IS a lease, even though there is no written lease in place. There are facts not present here, such as, is your friend going to "pay" your mortgage for you? Why didn't the HOA approve the hardship lease? What are the consequences if the HOA takes the position that it IS a lease? Will they suspend your voting rights or can they deny your "tenant" access to the amenities? If there is a concrete basis why they denied the hardship leasing permit, is this something you can address? The simple answer is that the mere absence of a written lease does not mean that the property is not being "rented" out and the HOA may, correctly, assert that you are leasing it over their objection.

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