It would better if you could supply 1.0V instead of 1.2V as the core voltage is 1.0V.
That really does not answer the question. I believe the L option is only a speed binning of the devices, and the L devices are faster devices that can meet the timing specs even when operating at lower voltages. This is an issue of parts availability. The existing design uses non L parts, but L parts are available.
Apologize for the misunderstanding, for your information, L parts means low voltage device and the device is designed to work with core voltage of 1.0V. Thus, it is recommended to have 1.0v supplied to it.
We have accidentally done this (wired 1.2 V to VCCINT for Cyclone IV low voltage device) and this design has been running for 10 years.
I was looking on forums to see what this does to timing analysis - I believe it would help (fortunately). I am having problems meeting setup timing in TimeQuest right now.