Nintendo Switch Lite controller will not connect or keeps disconnecting

A Switch Lite has its buttons built in, so a controller problem here is either a built-in control that misbehaves, such as a drifting stick, or an extra controller that will not connect. For drift, where the cursor moves on its own, start by recalibrating the sticks in System Settings, Controllers and Sensors, Calibrate Control Sticks, and clean around the stick gently with isopropyl alcohol on a cotton bud; drift that survives that is a worn part. Extra controllers pair differently on the Lite, because it has no rails to attach Joy-Cons to: use the Controllers menu, Change Grip/Order, and press the sync button on the controller, or pair a Pro Controller by its sync button.

If a controller will not connect, check its battery and that Airplane mode is off. Drift on a Switch Lite is a known wear problem on the thumbsticks, and Nintendo has repaired drift on Lites, so a console that is still within a warranty or that Nintendo will repair is better sent in than opened at home. Mild drift often improves after a recalibration, so try that first and test with the controller test in System Settings. Stick drift often worsens slowly, so note when it started and whether it affects one direction, which helps Nintendo's repair staff decide what to replace.