I tried to make cheap guitars into an LP, getting mahogony guitars (ie Parker PM20 Pro) and the pickups (Gibson 57, 59) but when a guy came over to buy an amp, he had a lefty Gibson LP Traditional and it sounded better than any guitar I ever had or made with humbuckers.
So I bought a 2012 and it sounds fantastic. I bought another, use 2012, to see if it was the same. It sounded/felt exactly the same. (Sold that one)
They PLEK the neck, so they don't seem to get the complaints pre-plek get. But man, recorded, live, it GROWLS like no other guitar and has an authority on solo's that my other way better built guitars (ie Thorn) just can't seem to achieve.
It's magical and it's own thing. I hope your LP-Like is a copy enough to have that mojo!