Speakers for Luxman LX-380

Most likely a high efficiency speaker such as Klipsch, JBL, ZU Audio etc.

Right but looking for specifics.

I own many speakers. The ones that sound very good to my ears using my Allnic T-1500 300B Integrated are (in no specific order) Klipsch Forte III, JBL 4319, Von Schweikert 99 with Super Tweeters, ZU Audio Union Six Supreme, and Montana EPX speakers. Different flavors but all sound very good.

OP,you need to provide a lot more information...What is your budget?How big is the listening room?What are the acoustic properties of the room,ie:bare sheetrock walls/lots of glass/hard floors or carpet/lots of overstuffed furniture or barely any?What kinds of music do you listen to & how loud do you listen?Will you add even a basic amount of acoustic room treatments at a later date?
With your amp having only 18wpc.@ 8 ohms/20wpc.@ 6 14wpc.@4 ohms you want something that doesn’t drop below 6 ohms throughout it’s entire operational frequency range..
If you have a smallish room,say something around 12’ x 14’ (+-2’),listen to a variety of music at normal levels with an occasional rock out mode,my recommendations without knowing anything else but your amp,I would say ProAc Response D2,Harbeth M30.2Xd’s,Spendor Classic 3/1 or Reference 3a DeCapo with the factory available silk dome tweeter instead of the Beryllium version...

@freediver  just asking a general question. If you have one or heard one what speakers? Did it sound good to you? 
 

just looking at which direction to go.

I'd imagine that the Heresy IV's listed with your system would sound good.

Though only 10 watts Coincident has an interesting single ended EL34 based integrated amp for approx. half the price of the Luxman (they sell direct).

DeKay

Oops. I was going to recommend Sonus Faber… but that am- has very little power. You’ll need a specialty speaker that sounds good with very low power..

Klipsch Forte IV

I have this fantastic amp and have the following speakers: Devore Super Nines, Harbeth 30.2XD, Dynaudio Heritage Specials and Magnapan LRS. The Maggie’s sound terrible with this amp but the other three sound great. I probably play the Super Nines and Heritage Specials the most in a rotation. My Luxman is currently in storage because I recently bought another amp and have too much  equipment. I’m considering selling it so if you are interested let me know. Mint condition.

First, that Luxman L380 is a gorgeous piece of equipment!  20W of tube power is enough to make excellent sound with a huge variety of reasonably efficient speakers.  Just avoid small ones that try to have deep bass…and adjust your volume expectations accordingly.  I have a Dynaco ST35 and it sounds great with IMF Super Compacts in a medium sized room (2000 cu.ft).