For determining your stats on the weapons, your professions are the important thing, not the skills. The skills are what you need to build up those professions, but the profession levels determine how well you can use the gun.
With those stats, you must not have reached the recomnmended level for the LR32, which needs Level 16 in Ranged Laser (Dmg) and Laser Sniper (Hit) professions.
If you're following the (L) skilling route then you need to gradually move up to higher weapons as you go along. For the fastest skill gain you should try to use a weapon that gives you Skill Increase Bonus, i.e. you have reached the recommended levels but haven't maxed out the weapon. For best eco you should always use a gun that you've maxed.
From UL2 the next step would be Riker UL3 or Breer M4A, I think (but don't quote me on that, I don't generally use laser rifles).
The best thing to chip, to raise your damage professions, would be Laser Weaponry Technology, but I'd suggest just carrying on skilling with the appropriate weapons and let your skills build up naturally.
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