I never said it's "lite". I can say for certain that in my experience, when writes start to go up, such as stock market event stream coming in, sqlite3 doesn't perform as well as postgres, and scaling writes is hard in sqlite3. But I have no issue scaling Postgres for those data.
If you say, sqlite3 is good enough for most webapps, then I probably agree. But I would not use it for a lot of things that I use Postgres for such as pubsub, or really high transaction rate.
It's more complicated than "doesn't support multi-core" which you can see in the other replies here: generally unlimited concurrent readers are allowed with single or at least finite writers. Depending on a bunch of settings (e.g. WAL) you might also get concurrent writers, multicore sorting, and some other things that can cross cores too. Those things do have their own tradeoffs.
But my actual claim is that most things don't need to be "scaled" at all. And if you do get there, and again statistically you won't, then you're definitely going to be doing some other rearchitecting anyway and moving sqlite->postgres might as well be part of that.