Can I safely place a 60w between a 50w LED and a large heat sink that can dissipate 100 watts?
Your 50-watt LED requires a heatsink, because otherwise it would overheat and destroy itself. The temperature of the LED is directly related to the thermal resistance between the LED chip inside the package, through the heatsink, to the ambient air.

Your Peltier device will add a considerable amount of thermal resistance to this path, which means that your LED will run much hotter with it than without it. This is probably not a good idea.

Furthermore, Peltier devices are not very efficient at converting heat flow to electricity. If you need electricity for some reason, you'd be better off tapping what you need from the LED power supply itself.