I am above average (by a small margin) on Lichess, and it sounds trite but to be average at chess you have to not make blunders.

Things like not leaving a piece hanging undefended, not falling into one move tactical traps (forks/pins etc.), and learning how to check mate.

You can achieve all of that by playing slower games, and doing some puzzles.

Like the other comment said, usually being careful not to hang pieces and capturing hanged pieces takes one a long way. The most applicable advice is to count attackers and defenders in a particular square (or piece) and if you have more attackers than defenders then it is safe to move there, generally.

I was being (slightly) flippant. As in any other discipline you do need to actually learn some things: tactics practice, basic endgames, basic opening principles.

But that's different from opening theory and what people usually mean by memorization. It is almost all pattern recognition and rules of thumb, and all the opening theory memorization in the world won't help you if you dont understand the ideas behind them. All the top players are extremely sharp tacticians long before they do any memorization.