As pointed out in the "New initiative rules in the Legendary Edition" thread on the Lords of Lemuria web forum, BoL's current initiative rule (roll 1d6, add Agility, act in descending order from highest total) seems out of place when compared to the usual model for tests in the game (roll 2d6, add attribute, add career if applicable, check for Mighty Successes and Calamitous Failures).
We'll therefore be using a variant of one of the house rules suggested in that thread. Heroes and NPCs will check initiative at the start of combat; their results will stand for the duration of the battle (unless something in the fiction of the game happens to necessitate a new initiative check). Each participant (or group of participants in the case of NPCs and creatures) will roll 2d6, add Agility, and see if the result beats the standard target number of 9. (A player can ask to apply a relevant career bonus to this roll; however, if the bonus is granted, that career cannot be utilized again in the ensuing combat.) Results should be read as follows:
Calamitous Failure = Unable to act in the first round of the combat; thereafter always goes last.
Failure = Acts in descending order of total result after all successes have gone.
Success = Acts in descending order of total result after any Mighty and/or Legendary Successes have gone but before any failures may go.
Mighty Success = Gains an extra action in the first round of the combat; thereafter always goes first (unless someone spends a Hero Point/Villain Point to gain a Legendary Success).
Legendary Success = Gains two extra actions in the first round of the combat; thereafter always goes first.
The extra actions for Mighty and Legendary Successes represent "getting the jump" on the rest of the combatants. Ties are broken according to the rules provided on p. 36 of the Legendary Edition (but Mighty Success and Legendary Success totals always trump regular successes, even if the regular success total is numerically higher).