The top ten garden games need a Lawn and a gardener who bites their tongue occasionally.
French Cricket the game where the feet must stay still and together and the ball is bowled at the feet from wherever it lands. Hitting the ball into another garden or favourite bush is 6 and out except there is no scoring anyway.
Tip it and Run is a short version of cricket with an L shaped pitch where the bowler bowls at the wicket as soon as they have the ball and a batter has to run at right angles a defined distance and back if he tips or hits the ball anywhere.
Croquet need some equipment similar to that show which can be bought from a sports or toy shop or from Amazon.
Carpet Bowls or even bowls if your lawn is large enough. The fun is in the bias that makes the ball roll in a curved line. Unless the grass is very wet it is unlikely to damage the lawn.