If I were to try to do a warlord in 5e, I'd probably do it like this. There are really what? Two versions of warlord? Inspiring and Tactical? I think the BM does a pretty good job covering the tactical part, so I'd create a new Inspiring Warlord subclass modeled similar to the battlemaster. Fewer maneuvers, but the PC knows them all.
Combat Leader
You and each ally within 50ft who can hear you gain a +1 initiative bonus.
Inspiring Leadership
Leadership Dice: You have four leadership dice, which are d8. You can use inspiring leadership dice on any Inspiring Action below. You know all of the Inspiring Actions. You regain leadership dice upon completion of a short or long rest.
You gain another leadership dice at 7th level, and another at 15th level. Upon reaching 10th level, these dice become d10s, and at 18th level, d12s.
Maneuver save DC = 8 + your prof bonus + CHA bonus
Battlefield Leadership
Starting at 7th level , you and any ally within 50ft gains a +1 bonus to any saving throw.
War Leader
Starting at 15th level, if you roll initiative and do not have any leadership dice remaining, you regain one leadership dice.
Inspiring Actions
Make the Save: Roll one leadership dice. You or any ally within 50ft can take a reaction when forced to make a saving throw. Add the result of the leadership dice to that save.
Back in the Fight: Roll any number of leadership dice remaining. As a bonus action, add the result of the die roll + your CHA bonus as temporary hit points to yourself or any ally within 50ft.
Lessening the Blow: Whenever an ally within 50ft who can hear you is attacked by an opponent, spend a leadership dice as a reaction. The damage the ally suffers will be reduced by the result of your die roll.
Taking Advantage: Whenever an ally within 50ft who can hear you makes an attack of opportunity, you may roll one leadership dice and that ally will add the result to his or her attack roll.
Battlefield Logistics: Roll any number of remaining leadership dice. As a bonus action, add the result to the movement rate of you or any ally within 50ft who can hear you until the start of your or their next turn.