I have lost my game card, and I want get the game for Pokemon Home, so I can send some shiny Pokemon to my Pokemon Sword game.
The good thing is is that your save game is stored on your Switch itself (as explained in this answer). Therefor, you can buy/rent/borrow a different cardridge of Let's Go Pikachu to access that savegame.
The bad news, is that you cannot transfer Pokemon to Shield/Sword yet. A new service, Pokemon Home, is not released yet. When Home is coming out, it should be possible. It is set to release 'Early 2020', so you've got some time to prepare.