No, no they should not. They only absorb moves aimed at them. Though Lightning rod will pull in electric type moves aimed at partners.
When a Pokémon with Motor Drive is hit by an Electric-type move, its
Speed is increased by one stage, and the move will have no effect.
This includes the effect of activating a Cell Battery.
Generations III and IV
Lightningrod forces all single-target Electric-type attacks in a
Double Battle to strike the Pokémon with this Ability. In a Single
Battle, it will only cause the Pokémon with this Ability to always be
hit by Electric-type moves, no matter their accuracy. Note that
Lightningrod cannot redirect Discharge, as it targets all Pokémon.
Lightningrod cannot redirect an Electric-type Hidden Power.
If Follow Me is used while an Electric-type move is being used, and a
Pokémon with Lightningrod is active, the Pokémon using Follow Me is
hit instead. Generation V
Along with its previous effects, Lightningrod also gives Pokémon
immunity to all Electric-type attacks, along with the paralyzing
effect of Thunder Wave, and raises the Pokémon's Special Attack by one
stage whenever they are hit by one. If the Pokémon is Ground-type, its
type-granted immunity will take place before the activation of the
Ability's new effect and the Special Attack will not be raised unless
it is holding a Ring Target. An Electric-typed Judgment is also not
affected by this ability.
Source: Experience and Bulbapedia