Do you use any form of Luck Points in your OD&D game?
Lawful characters could take their Charisma Score and divide by three and round up (but a minimum of 2 Luck Points even if your Charisma is less than 6).
Using one Luck Point could grant you the following things to simulate heroism in action. Where applicable it could not be for an Evil or Neutral or Chaotic action and on Lawful characters can use Luck Points.
Examples of using one Luck Point grants you:
Add +2 to an attack roll
Subtract -2 from a saving throw
Subtract -4 from your AC vs. one melee-engaged opponent for one round
Add or subtract 20% from a % roll
You could do this after making said roll.
If the PC engages in an evil or a neutral or a chaotic action, then they lose the Luck Point without gaining any benefit. They don't gain that point back until they have atoned for the action.
I like this for three reasons, it encourages players to not use Charisma as a dump stat, if you do anything other than 3d6 in order for stats.
It encourages players to take Lawful Characters.
It encourages team work which is, IMO, a basic of good old school gaming.