One has to coat the material to be set on fire with something that has low infrared absorbance (and thus low cooling through heat radiation) but high absorbance

One has to coat the material to be set on fire with something that has low infrared absorbance (and thus low cooling through heat radiation) but high absorbance for low wavelength (blue/ultraviolet). This is called selective coating. https://en.m.wikipedia.org/wiki/Solar_thermal_collector https://en.m.wikipedia.org/wiki/Solar_thermal_collector Combined with the lens, this might work.