There's no way to remove input lag.
Every single part between you and the game has a delay. Your screen has a delay of some ms before it renders what it has been asked to, your mouse has a delay before sending data to comp, your brain and eyes reaction have delay, your muscles have, the cpu and gpu have, the network has, etc.
Most importantly, you will always have a ping to the server (or, in this case, the other players). You have one in every single game, and there's nothing anyone can do about it. As stated already, it might be bad to some players on the other side of the world (maybe 200 or 300ms), and it's the most likely possible lag COH1 had. The only way to reduce it would be client/server with the server close to you, by region. Refer to Inverse post.
If the animation delay that was fixed in this patch is in the value of 0.5s (I don't know about it but I would assume), that is HUGE. It's 500ms. A ping starts to become bad above 100ms. All other causes I listed are usually below 100ms too. In this case, the animation would be the limiting factor and the cause of lag feeling by a significant margin.
There might be other issues due to poor communication process or other stuff, some might be fixables, and in the work by Relic. Maybe they are even more significant, I actually don't know.
What I know for sure though is that cancelling any animation that would take more than 100ms would be a huge improvement no matter what.
