It's as easy as:
1) Go to the Lawnmos league.
2) Click the down arrows at the top of the page next to Lawnmos.
3) Click Club List
This then shows what teams are already taken and what teams are available a la:
4) Then click on Lawnmowermans name
5) In the pop up box that comes up (once you've clicked on his name) on the top right it says Send Private Message.
6) Click that and voilą job done.
Edit: depending on your account you might have a cap on the number of teams you can manage at any one time, so as Liam has said you might have to leave the Atletico job first before being able to join the Lawnmos league.