It has been a while since I looked at a 5e Warlord. There are many ways to translate the 4e Warlord into 5e. There is one way I find interesting.
The Warlord is a new class − not a subclasses. There are several Warlord character concepts to supply the Warlord class with its own subclasses.
To model the 4e feel, the 5e Warlord can use a spellcaster class as the chassis for the Warlord class. Wait. Wait. Hear me out!
The 4e Warlord mechanics used "powers" like the rest of 4e classes that also used "powers". The main difference was the flavor, themes, and occasional mechanical nuances, that depended on the "source", whether Martial, Arcane, Divine, Psionic, or Primal. (There were also other less developed sources, Shadow and Elemental, but Arcane, Divine, and Primal overlapped these.) The Warlord uses "Martial powers".
Powers had different refresh rates, "at-will", "encounter", and "daily". These powers correspond roughly to 5e "cantrip", "short-rest spell", and "long-rest spell".
The 5e Warlock is the best chassis for the 4e Warlord, because it has at-will "cantrips", encounter "slot", and daily "arcanum". Meanwhile the "invocation" can do anything from a daily feature to supplying or modifying an at-will feature.
Thus a 5e Warlord would actually have what is mechanically "Martial spells", but call these powers "exploits". Despite the mechanical similarity, the Martial effects are nonmagical. The effect and its frequency depend on how plausible its verisimilitude is.
The Warlord can and does heal, and with choice of exploits can even serve as a partys primary healer. But think of this as "restoration" rather than spontaneous faith healing. The "morale" restoration that relies on nonphysical hit points is only effective while the target has hit points. This restoration comes from coaching the target to keep the target alert and focused. One can watch any fightsport on tv to visualize how a coach assists a combatant. But once the target reaches 0 hit points, a real, catastrophic physical injury occurs, whether it is a knock out or life-threatening. Until then being "bloodied" is just superficial scrapes and bruises while the combatant starts getting punch-drunk and sloppy. But at zero, the "morale" exploits are less effective, if at all. At this point, the Warlord must switch from morale boosts to being a combat medic, using the Medicine skill checks, or analogous medical exploits, that involve smelling salts, bandaging, or trauma treatments.
Using the Warlock chassis, most of the Warlord features will be at-will or per short rest. So the normal feel of a Martial character remains intact. The Warlord relies on effort and runs out with fatigue.
Any situational exploits need a mechanical requirement for a specific opportunity to present itself. For example, some exploits only work if the target is at a disadvantage. Compare the Rogue Sneak Attack. Such situational requirements help the narrative of a Martial exploit feel more plausible.