Question Author
Well done, geevo, and thanks also to emmie & bobbin.
There are six 4-letter grid positions but three can be ignored as they contain the given letter, L. Only one of the three remaining possibilities has a very rare letter in first position, very common in second and fairly rare letters as the last two.
After that, the puzzle works out easily so long as you make the right choices between 1 & 2, and between 9 and 18.