As there has been lots of talk recently that in coming winter there could be shortages of electricity so that made me thinking some sort backup light wouldn't hurt just in case. I already have UPS to back up sone computer stuff so I was thinking some simple setup consisting relay with NC contact to control a lamp. Now the question is how normal everyday E27 LED lamp likes modified sine wave produced by UPS?

Unless it uses thecapacitive dropper, it should be fine.
Tocheck it,try to feed the LED viaa Graetz rectifier (by the rectified, but not filtered mains). If it lights normally, the LED starts with a rectifier (and then follows by either a linear regulator or a SMPS, but thatdoes not matter), so it will work fine. If it just flashes and then barely glows (or not at all), it uses a capacitive dropper (or something similar relying on a sinewave shape), so it can not be operated onthe MSW from the UPS.