Hi (a first name would be perfect)
A warm welcome to this great forum of Märklin fans.
Because LGB require more power, using the programming track (only one Ampère available) may cause you issues.
Using either MFX or DCC allow you to use the main track output (with full CS3 power)

The CS3 is indeed suited to drive an LGB loco but you need 2 things:
1 - the appropriate power supply (PSU) ( a 60101 for Europe and a 60195 for USA and Canada) that delivers 100 W
2 - you need to declare on the CS3 the Powersupply type you are using (60 W or 100 W)

Even if you have the proper PSU, failure to declare it will result in the CS3 declaring an overload past 60 W
Here is the CS3 screen where you select the PSU type

You must select the 100 W LGB PSU L51095 not matter if the primary voltage is 120 VAC or 230 VAC

Seems bizarre but it is simple in reality:
- select the PSU for your country (US plug and 120 VAC) for 22 VDC, 100W
- select the current on the CS3 so that it won't switch off too early

Cheers
Jean