Download the Lambda Client installer from the official source
Open the installer file
Select the Minecraft version you want to use
Make sure Java is installed on your computer
Run the installer and wait for it to finish
Open the Minecraft Launcher
Select the Lambda Client profile if it appears
Start Minecraft using that profile
If needed, place the client files in the Minecraft mods or versions folder as instructed by the installer
Launch Minecraft and verify the client is loaded