Take advantage of your slower firing rate to plan your shots. Both the Lex and Lex Prime are optimal long-range pistols.
Build upon the strengths of the Lex Prime (damage, critical chance, status chance) and learn to compensate for some of its weaknesses (fire rate, recoil, reload speed, magazine size) without mods.
Modding for all of the weaknesses could reduce the potential of building on the Lex Prime's strengths.
Alternatively, with maxed out rate-of-fire mods and maxed out reload mods, the Lex Prime can work as a close quarters pistol. However, beware of the high recoil when shooting it fast.
As with the standard Lex, Steady Hands can be used to counteract this weapon's high recoil.
The effects of the recoil are eliminated by pacing one's shots.
Steady Hands however is still very useful to quickly place follow up shots onto the target which will be necessary in high level where even fully modded, the enemy is capable of surviving at least a single hit from Lex/Lex Prime to the head, this is especially crucial if the weapon is not modded for close combat.
The Lex Prime pairs well with close quarter or otherwise less accurate primary weapons, to cover ranged enemies.