Yes. Just recently did this for a customer on LFS/LFFTS 11. 

First, bind a valid TLS certificate (with Server Authentication role) to port 5053 on the Laserfiche Full-Text Search (LFFTS) server.

The only UI I'm aware of that lets you enable TLS for LFFTS is the Laserfiche Administration Console "Register Repository" wizard. There may be some alternative way of enabling it for an already registered repository, but I've looked pretty hard and haven't found where that setting is stored.

So in Admin Console:

1. Take note of all relevant repository settings (SQL Server, database, repository directory, audit directory (if different), etc.)
2. Detach the repository
3. Reattach the repository, making sure to check the "Use SSL/TLS" box on the search engine page
4. Set a recurring reminder to renew and rebind the port 5053 certificate for LFFTS before it expires. Automate this if possible.