There are 2 issues with the new dials in terms of cut outs...one can be negated the other you will have to live with...
The thickness of the top plate is thinner but the amount of lume increases the height and so you lose the depth....Given the lume on these are not accurate in terms of uncharged colour...you should be considering getting it lumed anyway.. Dont get me wrong it is a decent rep lume but it is a very dirty colour in an uncharged state...
Or if the bottom plate of LH dial is decent, They do vary, then you could try swapping...
If you are considering the LH dial overall then you would need to say which version of his dial you have...
LH did 3 dial variants of note...but he did vary some dials between production because he was doing them on an individual basis so there are consistency issues as with all reps that are modded...so you can see differences in sheen/dial finish, dial texture, as well as Fonts, and inscription colour etc Also his lume varied in terms of quality, thickness etc..
Some of his dials I have seen in my hand are IMHO much better than the current dials but I wouldnt say thats a rule in terms of consistency... Plus some that have been preowned have been modded so you could find an LH with new lacquer coat etc etc.