Hey Simon 
I have a Nutmeg LISA and am probably weighing up the same debate as yourself!
Just as a disclaimer you won’t be able to open another Stocks and Shares LISA so anything you open in the Stocks and Shares world you would have to account for the tax implications (unless you open a SIPP (I think?)).
Diversifying isn’t necessarily a bad thing - and building your own portfolio can have its benefits. Quite a lot of information was put on this thread: Which stocks and shares app is best? so that may help you!
I think it all depends on your circumstances, what are you saving for, what are your goals with your money, how long do you want your savings to be “unaccessible” for. There are a lot of things to consider.
In terms of research and understanding of where to invest you’ll find a lot of information on previous threads on the forum.
Hope this helps, although not very decisive on what you should do - but that’s because it is your money!