I got Ultima IX because I was curious. I never played Ultimas, so I thought I might enjoy the game, I have no idea about the lore it ruined, as fans seem to say :)

The only problem I have with the game so far relates to the controls. They're incredibly unresponsive and clunky. There always seems to be a delay after my input, and sometimes my character keeps moving forward/in some direction long after I stopped pressing the keys.

Is this a known issue? Is this how the game always worked?

Played U9 when it first came out, so on a much older / slower PC and don't recall there being any control "lag" issues. On a modern-day system, should be even less so. Check you are patched up to version 1.18F (would presume GoG pre-patch their release but no harm checking). There is also a 1.19f unofficial patch (aka, made by one of the developers reportedly off their own bat, in their free time etc).

There are also a few fan-made patches around which you might want to consider that on the whole create a more balanced and IMHO more enjoyable experience. Be aware that patching the game will likely require a restart of your game (ie, loading a save game from a previous version probably going to cause strange things to happen).

Being a long time Ultima fan (can proudly state I bought, played and finished each one since the first one), the fact you don't know the lore is probably a blessing, I was one of those many outraged fans at the sheer disrespect U9 had for all that can come before it. For you, you can just enjoy the experience, U9 was rushed too soon out the door, it needed more time, care and attention to detail, but you should still have fun with it.

I'm also experiencing the same control issues (unresponsive, permanently walking forward with no input) regardless of which patch is applied. I bought Ultima IX upon release and don't recall these problems back then, but they certainly exist in this version.

This is a long shot but you might want to remove any headset or controller attached. Those will sometimes really mess with games.