You can buy drains that get cut into the base rail on your lanai.
These were invented and patented by a Villager who lived in La Reynalda off of Chula Vista in the Spanish Springs area. I believe he has passed but his children are running the business.
I installed 4 of them for someone last week. I think they will also install them, but I don't have any idea what they charge. Each drain costs $37.50 after tax.
Screen Room Drains - One & Only Patented Screen Room Drain