There is a mod on the site that changes the type of Laser 'bullets' in the Laser Defence equipment to Laser Tower laser 'bullets'.

https://mods.factorio.com/mods/Doomquill/Personal%20Laser%20Turret

It was very easy for me to 'edit' Mk.2 and 3 LD your mod adds to this standard.

LD's already use Turret lasers in their recipes. This small change will make the laser shots in the LD equipment, logically, more powerful with Laser Turret damage upgrades.

You could add option in mod settings when in game to allow Mk.1, 2 and 3 lasers to use same tech as Turret lasers.

I've looked into it, and I've added an option to allow all pld's in the game to use the laser turret upgrades. Due to the power of mass pld's even without upgrades it is defaulted to off. You need no other mods to make it work.
Cheers and have fun

Thanks! :D