How the bullet is constructed, where it hits the animal, and how fast it was going upon impact is ultimately what matters most.
The max lethal range depends on all those things. The starting velocity also matters, as does the bullet's BC which determines how much velocity is retained as its traveling down range.
How the bullet is constructed and how it is designed to perform terminally (its mechanisms for such) will be the main factor in determining max range.
In general, softer constructed bullets with a high BC will give you the absolute most range due to requiring less impact velocity, and thus force exerted back unto the bullet, in order to expand sufficiently and still produce adequate hydraulic force and thus adequate wounding for a quick and clean kill.
There can be trade offs to this though, since we can't always predict not guarantee our shots will only be long range. So we need a bullet that can perform properly at close range and higher impact velocities too. The best way to achieve that is to run a heavy for caliber softer constructed bullet with a high BC and at medium MVs. The high BC will ensure you still have good range, yet the higher bullet mass and only medium MV means close range shots work out well too.
As far as energy…. Energy, in regards to the calculated kinetic energy of a bullet at a particular velocity, is only a potential. It's only a potential in regards to it depends on how the bullet behaves upon impact and how it thus transfers that energy and puts it to work. Not all bullets put the energy to work or transfer it all. A bullet that punches or pencils right through, for example, did nothing in regards to putting energy to work and didn't transfer hardly any of it. This is why there's confusion and two sides to this argument on whether energy matters or is relevant. Yes, it is relevant, but bullet construction and impact velocity do matter more in the grand scheme.
So to expand upon the subject of energy specifically, energy goes to work by converting to force. Not all bullets turn their energy into force, or at least not a lot of force. Some are much better than others and need less energy to begin with. How they convert energy to force is highly dependent upon their construction and the mechanics of how they behave terminally.
This is where the terms energy dump and energy transfer come in. As a bullet converts its energy into force, it rapidly loses momentum. If the bullet loses all its momentum from producing a huge amount of force, it typically doesn't exit. Typically, the higher the rate of momentum lost, the more force is produced and more wounding occurs. That said, you still want to balance it all out so that it occurs within the chest cavity and does the most damage to the vitals. You don't want the bullet to lose all its momentum on or near the surface, for example.
Also, the more momentum the bullet still has, the more force it's still producing. If it produces a ton of force, but simply doesn't lose it all at a rate higher than the speed its traveling, it'll still exit, which we see still with certain soft constructed lead core bullets in certain scenarios.
Ultimately, knowing how the particular bullet you're wanting to use coverts energy into force is what you should focus on and will be much more helpful than going with just a basic rule of thumb on minimum energy. There are many bullets out there that will produce excellent wounding with well under 1000ft-lbs of energy. That's because they're highly efficient at converting energy into force. Conversely, there are many bullets out there that are not efficient at converting energy into force or don't convert very much of it into force.
Frangible (soft constructed) bullets are very efficient and effective at converting energy into force. Getting that proper balance though is crucial, and achieved by having sufficient starting mass and not placing the shot in an area where the amount of impact resistance is too much for the impact velocity. But an adequate amount of mass at the start can really help with that, as does adjusting shot placement for close range shots. A well-constructed and properly selected frangible mono can be very effective as well, to be fair to those types.