I've added a page to the wiki, but it's still a bit vague:
http://aurorawiki.pentarch.org/index.php?title=Laser_warheads

Can anyone who has experience with LWHs elaborate?

I can.  I just tested them out in 7.1, and they don't work.  They are not immune to final fire at the moment.  They may be supposed to be, but that feature is broken.

You could just evaporate the crew with conventional missiles if they worked the way you think.

Radiation does nothing to crew.

Ahh, that sucks. So enhanced rad laser warheads have no purpose then. I wish that crew could be killed by radiation weapons, that should be a feature (I'm going to post that in suggestions)

Ahhh, I think I found something too cruel. I just researched laser warheads in my game and I noticed you can have both laser warhead and enhanced radiation checked at the same time. Does this mean you can shoot radiation beams at enemy ships to melt the squishy organics inside (to capture the ship with minimal resistance) while dealing almost no damage to the ship itself? Soft x-ray does 10 rads per msp and only .4 damage. In my opinion, this could be a little abusive if it works the way I think it does. But then again, maybe radiation does nothing to crew in space.

Most interesting. That said, it would be nice to have the laser warhead techs for the upper end laser wavelengths, because the base damage gap between normal warheads and laser warheads get really bad at higher tech. *hint, hint*

But yeah, these results prove themselves quite interesting, if still rather limited in usage, specially because of the uncontrolled sandblast effect. If there was some (even limited) control of how many laser warheads there was per warhead MSP in a given design, it might become quite the fair alternative to normal warheads.

Laser missile tested against target with CIWS (tracking speed 100kkm\s, 2 shots).

Missile Size: 12 MSP  (0.6 HS)     Warhead: 100    Armour: 0     Manoeuvre Rating: 27
Laser Heads: 10
Speed: 8300 km/s    Engine Endurance: 34.6 hours   Range: 1 032.7m km
Cost Per Missile: 30.25
Chance to Hit: 1k km/s 224.1%   3k km/s 54%   5k km/s 44.8%   10k km/s 22.4%
Materials Required:    25x Tritanium   5.25x Gallicite   Fuel x1250

Development Cost for Project: 3025RP
CIWS doesn't want to shoot. Neither missiles nor warheads were engaged by CIWS.

1st January 2025 00:31:01,TE,Sol,Tribal 001 - Missile Fire Control FC24300-R100 targeting Karabane 007 at 3 100k km
1st January 2025 00:31:01,TE,Sol,Size 12 Missile Launcher (x1) has launched a Size 12 Anti-ship Missile. Reload Time: 30 seconds.
1st January 2025 00:31:06,Test-2,Sol,Hostile Missile Contact TCS 12
1st January 2025 00:37:16,TE,Sol,Salvo of 1x Size 12 Anti-ship Missile has intercepted its target. Chance to Hit 100% (Target Speed Zero)
1st January 2025 00:37:16,TE,Sol,Karabane 007 hit by 10 points of damage from Size 12 Anti-ship Missile
1st January 2025 00:37:16,Test-2,Sol,Victory 006 hit by 10 points of damage from Size 12 Anti-ship Missile
...
1st January 2025 00:37:16,Test-2,Sol,Nuclear Detonation: Strength 10 detected! (x10)
1st January 2025 00:37:16,TE,Sol,Nuclear Detonation: Strength 10 detected! (x10)

P. S. Conventional gauss guns failed to work in final fire mode against laser missiles. Area defense laser cannons did fine.

Ok, set up a test debug save, and got some results out of testing:

From what I can see right now, using laser warheads is pretty much the equivalent of sandblasting the enemy ship: That is, it takes the total (reduced by the laser warhead) warhead value of your design, divide that by the number of laser warheads in it (one per warhead MSP), doing one explosion of that size for each laser warhead in the design. So, if you have Extreme X-Ray Laser Warhead, the top tech for laser warheads (near gamma and up lacks the tech, at least for the time being or so it seems), you'd get one explosion per warhead MSP, each of strength 10 (assuming round numbers for warhead MSP, it can be different, specially at small missiles if you are not doing so), each the standard form for a missile.

For fleets at least, those multiple explosions only hit the targeted ship, and don't seem to spread through the whole fleet: If it were otherwise, it could be an interesting anti-fighter instrument. I've yet to test it against missile salvos, but if it does work, it could have a rather situational use against large salvos. Otherwise, I'd say it's only useful if you are focusing nearly totally on energy weapons but want a decent warhead anyway.

But anyway, more to come soon after some extra testing.

Edit1: Against Missile Salvos: Effective, it destroys as many missiles as there are laser warheads (or at least it does so if the missile in question completely sucks, with ridiculously low speed, no armor and the like).

Edit2: And confirmation on fighters: It doesn't work. Even if it destroys a ship entirely, it does not move to the next ship in the task group.

So, yeah, from what I've seen it's only real use for now it's to re-purpose large missile launchers into anti-missile duty and some occasional use in boarding.

yeah isnt part of the point that they close to a range, then "blow up" firing a laser blast of whatever strength at the target ship from outside of CIWS range?

I have tested the laser warhead missile against enemy ship with exactly one layer of armour.
The specifications of missile:

"Flare" Size 5 Laser Missile

Missile Size: 5 MSP  (0.25 HS)     Warhead: 6    Armour: 0     Manoeuvre Rating: 20
Laser Heads: 1
Speed: 120000 km/s    Engine Endurance: 28 minutes   Range: 203.4m km
Cost Per Missile: 10
Chance to Hit: 1k km/s 2400%   3k km/s 800%   5k km/s 480%   10k km/s 240%
Materials Required:    1.5x Tritanium   7.8x Gallicite   Fuel x2500

Development Cost for Project: 1000RP
One laser warhead missile was launched to the enemy gatebuilder. The missile successfully engaged the target:

8th January 2208 23:58:21,ZemSoy,EZ Aquarii,F-Settembrini II 003 - Ratters ASM Launcher Assistant R100\Sz1\T5 targeting Centurion 021 at 25m km
8th January 2208 23:58:21,ZemSoy,EZ Aquarii,Hit-and-Run ASM System Mk. 2 (x1) has launched a "Flare" Size 5 Laser Missile. Reload Time: 2145 seconds.
9th January 2208 00:01:56,ZemSoy,EZ Aquarii,Salvo of 1x "Flare" Size 5 Laser Missile has intercepted its target. Chance To Hit 914%: (Missile Speed 120000 km/s / Target Speed 3519 km/s) x Missile Agility 20 x GradeBonus 34%
9th January 2208 00:01:56,ZemSoy,EZ Aquarii,Centurion 021 hit by 6 points of damage from "Flare" Size 5 Laser Missile
9th January 2208 00:01:56,Invader,EZ Aquarii,Gateway 015 hit by 6 points of damage from "Flare" Size 5 Laser Missile
9th January 2208 00:01:56,Invader,EZ Aquarii,The ship has no shields
9th January 2208 00:01:56,Invader,Unknown,As a result of combat, the crew grade bonus of Gateway 015 has increased to 0.58%
9th January 2208 00:01:56,Invader,EZ Aquarii,4 damage absorbed by armour.
9th January 2208 00:01:56,Invader,EZ Aquarii,Jump Gate Construction Module - 30 remained intact on Gateway 015 despite receiving 2 points of damage.
I've expected damage pattern to be 3-1(-1-1), just like the actual laser with 6pts damage, but what I got is 4-2 damage pattern, just like the actual missile with 6pts warhead.

Therefore, the laser warhead missiles seem to act just like the weaker version of conventional missiles, meaning they're useless.