the lamp is an LED
The device in the picture is an electronic "transformer" designed for halogen bulbs. These devices in general are not suitable for anything other than a halogen lamp. It is not likely suitable for an LED.
There are halogen replacement LEDs which are specifically designed to work off an electronic transformer. I installed them in my parents' bathroom, which has 12V fittings, each with an electronic transformer, about 10 years ago and they're still going strong.
I suspect that's not the case for the original poster.
the lamp is an LED
What sort of LED? Is it a halogen replacement LED?
Are you having problems getting it to work?
As mentioned above, the replacement transformer you've selected is an electronic transformer. Rather than a big heavy low frequency mains transformer, it uses a high frequency oscillator to drive a small, ferrite cored transformer. The output will be a high frequency, typically 20kHz to 100kHz, modulated by double the mains frequency. The LED must be specially designed to work with an electronic transformer. If you can't find any data on the LED, then it's safe to assume it needs 50Hz to 60Hz to work and is incompatible with your electronic transformer. If replacing the LED with a suitable one isn't an option, then you need to find a mains frequency transformer.
One helpful hint in looking for mains frequency transformers, is to avoid anything which is designed for halogen lighting and if you do find a lighting transformer, check it's toroidal and the weight. Electronic transformers are much lighter. A 40VA mains toroidal transformer will weigh about 500g. If it's much lighter, then it's definitely an electronic transformer.