Using power formula for DC circuits: Power [Watts] = Voltage [Volts] x Current [Amps]
If you are stuck with USB 2.0, then you are limited in how much current you can draw by the USB 2.0 specifications, which is 2A @ 5V, for a total of 2 * 5 = 10W.
So, you then need to increase the voltage using what's called a boost converter, which will boost the voltage up to a certain level; but unfortunately the total power you can draw still depends on the USB port, that being 10 Watts.
If we assume a 100% efficiency of the converter (ideal), when boosting from 5V to 12V and having 10W available, we will get 10 / 12 = 833 mA maximum output current.
Since the product page of the first lamp says that 1 Amp of current is required at 12V, i don't think you can ever hope to power said lamp with a USB 2.0 boost converter.
I tried to look around for a USB 3.0 boost converter with support for the Power Delivery protocol, but couldn't find any: these would support higher power, but would in turn require a USB 3.0 power back with Power Delivery protocol support.
They also might be more expensive.
Meanwhile, you could check with a multimeter the output of your USB 2.0 boost converter to see if it still works, and saved itself thanks to internal over-current protection, or if it's actually dead.