Do you want to access the SC in MCO or FLL? It sound like MCO. It appears the gates for Spirit and Delta are in different satellites (Airside 3 and 4) served by different TSA checkpoints. You can probably ask the TSA if you access Airside 4 to use the Delta lounge. Of course, you'll need to go back through TSA to get to the Spirit gates.
Thank you. Exactly what I was looking for.
Bman