Yes. I have one of these. (The Hornady LNL Progressive press's) I've had my Hornady LNL for....ghee....like about ten years now. I've kept mine up to date with the EZ-eject "system" (Hornady sent me a new bottom plate for free when I ask. Mine was new enough that I didn't have to pay for it.)
If you look at the description on MidwayUSA
they pretty much tell you what the initial press come's with. You get the "Die Bushings" (easy to swap dies in and out) but what you will need to buy for each caliber is (of course) the dies, and then you will need the die plate that gets bolted on the bottom of the LNL. Some die plates will do several different calibers, some just one. I have several. I have 44-Mag\Spec., .223-Rem\5.56, 357-Mag\38-Spec, 45ACP, and a few others that I can't think of off the top of my head. You will need the bushings for the dies for each set up as well.
What you won't need is a different powder drop for each different setup. Of course, you will need to adjust the powder drop when you do a caliber changeover.
As for dies, I have Hornady, RCBS, Redding that I use. Now, I do not have any Lee dies that I use on my LNL. I have Lee that I use on my single stage...and I honestly can't recall if Lee dies have any "issues" with the LNL or not. If so it would be in the die length. The new powder through dies from Hornady are great to work with. I also have a RCBS Lock out die (Not the Hornady "powder cop"...it's a POS) that I use to help monitor powder charges over or under. It's well worth the cost!!
Now, if your buying the new one with the EZ-eject system....do not buy any of the older plates (used or from Ebay from someone's old stock) that are not cut for the EZ-eject system. They will not work on the new EZ-eject model.
On my LNL I purchased the auto brass feeder. I like it as all I do is focus on placing the bullet on a powder case. And I rely on the Lock Out Die to "assist" me in catching any possible powder over\under charges. Believe me.....when the press just locks up....BANG...it gets your attention fast!!
If I didn't answer everything.....and likely so....maybe others will jump in. But, ask away if you have more questions.