In an option contract, the seller is the optionor and the buyer is the optionee. It is a unilateral contract in that the seller is obligated to sell, but the buyer has the option to buy.
When created, an option contract is a unilateral contract. But when the buyer exercises the option, it becomes a bilateral contract.
The option is assignable to another party unless the contract forbids it.
In a lease option, the lessee agrees to lease the property with an option to buy the property.
The option is usually given for some type of consideration. This can be money up front or added on to the rent amount to be applied to the purchase. The lessee would be the optionee and the lessor would be the optionor, as they are giving the option to purchase at a designated time.