Slice64 said:
The motor stops working, lights still on.
THen that means the battery's BMS is not turning off, it's just the controller stopping, probably due to LVC, specifically voltage sag under load.
What exactly is your battery?
Should be this one https://www.akkushop-24.de/Lithium-Ionen-Akku-48V-30Ah-1440Wh-Akkupack-incl-60A-BMS-Ladegeraet-wasserfest-fuer-Scooter-E-Bike-Pedelec_1 sorry that the website ain't available in English.
That's ok, google translate works on text ok.

I quoted their specs below. Looks like if it is what it says it is, it should be good enough to run the controller.
Lithium-ion battery pack 48V 30 Ah 1440Wh waterproof for scooter / e-bike
- Voltage: 48V
- Capacity: 30Ah
- Energy: 1440Wh
- LiCoxNiyMnzO2 / battery
- 18650 lithium ion single cells
- Weight: 8.1 kg
- BMS battery management system
- Temperature and overcharge protection
- Dimensions: 295 x 140 x 135 mm
- max. continuous discharge current: 60A
- max. peak discharge current: 180A (1-3 sec.)
- cut-off voltage: 35.75V
- charging voltage: 54.6V
- Battery 48V 30Ah waterproof
- Connection cable incl. 70A fuse
- Charger 54.6V 3A XLR/3Pin
The batteries must not be operated in series or in parallel.
BMS continuous current: 60A
What exactly is your controller?
https://www.ebay.de/itm/313870133119?var=612598202845 this nice ebay pal, had a different one before that came with the motor, but it died.
What little specs they provide are below
THey don't specify what the LVC is for each voltage, but it does say it autodetects teh battery voltage and sets the LVC appropriately. So if it is not detecting that correctly, it may set the LVC too high. Additionally it says it's setup for lead-acid, not lithium, which means it's LVC may be wrong for your battery (probably not, but it doesn't say what it is).
For 45v, it means they could be using an LVC of 11.25v per lead-acid battery (there'd be four of those in series for a 48v system; 5 for a 60v, which would then have an LVC of 56v or so). That would be higher than most, which are usually around 10.5v per SLA (so about 42v, just like a lithium battery).
It's more likely that it's still using a 41-42v LVC, but that your battery is sagging in voltage to taht point under load, when it's no-load voltage drops to 45v (so when you see the meter it is at 45v)
Specifications:
*Power: 1500W
*Optional Voltage: 48V/60V
*Undervoltage: automatic identification
*Brake: high / low level
*Phase: automatic identification
*Current limit: 40A
*Size: 9*4*2in (Approx.)
If you have a wattmeter, most of them store the Vmin, or lowest voltage seen during operation. This would tell you how much voltage sag you're getting, and whether it is low enough to trigger the controller's LVC.