I've never heard of 'L' 4, but the 'I' stands for 'inline', meaning a straight engine where the cylinders are in a single row, as opposed to a V configuration like a V-8. L could stand for 'lateral', meaning the typical front-wheel-drive transverse layout (where the engine is oriented right-to-left instead of front-to-back). I suppose it could also stand for 'longitudinal', meaning the cylinders are in a straight line as well, but that's probably not correct, given the TSX's transverse layout.
Are you sure they're not just calling it a 2.4L 4 cylinder? In that case the 'L' would be for 'litres'.
In any case, the designations you're looking for are '6M', '6MT', or MTX. These are all shorthand for 'manual transmission'.