Sucks this model is discontinued, and aftermarket sights never took off.

Glock front sights seem to fit perfectly and aren't much taller than the factory ruger sights.

Glock rear sights look like they will fit into the LCP Custom's dovetail, but seem to be too long.

I might just buy some Ameriglo Cap sights for $60 and use the front sight on the LCP Custom.

I know Ruger says not to remove the front sight. But its nothing a little blue loctite cant fix on re-installation.

Update:
Ameriglos have the threaded hole drilled to far down. Glock OEM Sights are perfectly centered.

What Glock sights did you put on-steel,night sights,etc.? Any difference in the height for shooting? I have one and want to do the same thing. I almost bought a fiber optic front sight but was on the fence as you were. My factory front sight (that is not supposed to be removed),actually removed itself and I had to buy a tool to put it back on. I thought this model would replace the standard model as it has needed upgrades-sights,bigger trigger and steel guide rod. I can't believe they discontinued it.

I did see a few new ones on Gun Broker.  $259 buy now price NIB.  Davidson's advertises them but has '0' in inventory.  I have LCP, LCP Custom and LCP II.   LCP II is higher priced, better trigger, but still hammer fired, now single action.

Hey sorry I haven't gotten around to posting back here. I was planning on getting steel sights but never got around to it. The main issue is I would only be using the front sight since the rear sight would be too wide. Even the G43 rear sights would be too wide.

The front sights appear to be the same height.

The trigger is pretty nice for what it is. I shoot the LCP Custom pretty well but I did add a Hogue Grip.