If you face the "Lost connection with anti-cheat" error constantly, then:
- Delete the BattleEye folder in the game folder and then do a file integrity check through the launcher
- Disable all anti-viruses and protection programs (for example, Windows Defender) for a while, and / or add the launcher and game to the white list
If there is no problem when using a different method of connecting to the Internet (another provider, mobile Internet, etc.), this means that for some reason your connection does not provide the correct connection. Contact your provider.