Constant LAN port?
Solution 1:
According to Minecraft's Wiki, you can use the /publish command.
/publish [port]
port: integer
Must be a 32-bit integer number. And it must be between 0 and 65535 (inclusive).
The port to host on. If not specified, a random port above 1024 is chosen.
Solution 2:
No, LAN worlds always use random ports. You would need to run a dedicated server to choose your port. You can move the world folder to the server and either rename it to "world" or change server.properties to use its name.