A lawful neutral Paladin would not follow the law
"like" a neutral good Paladin ... he would follow the
law of course. It says so in his contract(s).
A neutral good Paladin is halfway lost to the Slaadi
and follows the "law" for whatever silly reason they
come up with. Indeed, a NG Pally might be following
the law, only because of the influence of his mount.
Yes, a NG Pally's Horse can sometimes follow the law
better than the NG Pally.
We LN Pally's seek to contain such nonsense.
Lemme show you the manual ; on page 47a it says ...