No, the Hornady press conversion kit requires a larger die hole for the press conversion bushing that accepts LNL-fitted dies.
If you really want a hand press, I recommend the Huntington Compac hand press over the Lee. I started with a LHP, but switched because it was poorly manufactured, and not nearly as well designed as the Huntington. I put a small wooden base on my Huntington that lets it stand up on a flat surface when I need both hands for something else for a minute. It also has a built-in priming ram.
The LHP, with its hollow ram, works great with a universal decapping die, since it captures the spent primer and debris very well. Just don't let the hollow cavity fill up all the way, or you can't get the shell holder off of it to empty it. Don't ask me how I know this...
If lack of a permanent bench is your reason for wanting a hand press, consider getting a regular press, and mounting it on a 2x6 that you can then clamp to any table, counter top, etc. when you need it. It is much more convenient than even the Compac.
Andy