Is this the lichess of the Go world?

Sort of. OGS is the Lichess of the English-speaking world certainly. There are several much larger servers if you speak Korean/Japanese/Chinese, but they also have less in common with Lichess.

Back when I was playing, KGS was where everybody was playing. What happened? Just normal competition?

KGS is still going but still Java client only?

These days there are lots of great alternatives :

OGS, Fox, Tygem, Panda Net to name but a few.

All of them have their pros and cons but OGS is great for western players.

Also can highly recommend lifein19x19.com

Small correction: KGS is no longer Java-client-only. The protocol was opened up a few years ago and there are several web-based clients now, most notably https://shin.gokgs.com/

Also thank you for the lifein19x19.com shoutout :)

Yup, KGS is dying a slow death and was turned over to the American Go Association to be managed. KGS Plus is free now, which is a nice Plus, I suppose.

KGS is still huge, but OGS has been consistently adding feature after feature for years. At some point, my impression is that most English people just realized it has a nicer interface and better analysis and cheat-detecting tools. The main downside is a lack of high-dan players.

(I don't have data to back this up, just my experience as a roughly 1-dan player who hangs out with a lot of U.S. Go folks)

In my experience, KGS is nowhere near as popular as it used to be, sadly. Tournaments dried up, player base dwindled and it's not the same

How do you cheat at Go? The only thing I can think of is cheating by self-playing thus gaining illegitimate rank?

Just like with chess, when AI engines got very strong a few years ago, people started using them to find superhuman moves and win games. Now OGS will tell you how similar your game's moves are to what a computer would have played. Even professionals don't get above something like 75-80%, but I've lost a dozen games to people getting 95%+ on that metric.

You could cheat in many ways.

One way might be to use a Go engine to analyse the best moves for you as you play. Even for non online play this is already a problem with Chess games and hidden smartphones. Everyone has a 9d bot at their disposal these days. And of course one could make use of cloud TensorFlow if that’s not enough.

There are ways of detecting cheating.

Main way is using an AI to tell you what the next best move is.

Would you mind giving examples of these much larger servers? Japanese, preferably...

For Japanese go server, I'd suggest IGS aka PandaNet.

It's hard to say how much larger it is than OGS. OGS has an enormous population of correspondence players but generally smaller for live play maybe by 3x?

I would also highly recommend PandaNet. They have some really tough players.