>> how would the lease option work without paying off the underlying mortgage first?
A lease option would not be affected by whether or not you had an underlying mortgage.
But none of these possibilities would make sense without keeping the underlying loan in place (aka "wrapping" it). That's what gives you the leverage to make it a good deal. Otherwise you're just buying a home with no equity.
Whether you're doing a lease option or seller carry, the idea is to create cash flow. With an underlying payment of $1800 and income of $2400, you would be in great shape. And the buyer is responsible for the repairs and maintenance, so in that scenario you would have true $600/mo cash flow.
I've never invested in Texas but I have heard rumors that they outlawed lease options, so that's something you would need to look into. I'm guessing there's a workaround but you would need to consult with a Texas investor or attorney, or google/BP. If you're spending 20K then you would probably want to go with the seller carry instead of the lease option, so you could get a larger down payment from the buyer to recoup your money invested. But even if you had 20K invested, and you didn't recoup any of it, and you were cash flowing $600/mo, that's a 36% cash on cash return, not too shabby.