Yes. A large UPS, such as APC's Symetra, which provides "true sine wave output" can correct poor sine wave output but you may find it less costly to buy the right generator given that UPS batteries require regular replacement and aren't practical for "whole house" applications.
Low voltage within a certain range is not a problem but low voltage can be the result of poor frequency cycling which would be. You may have seen devices that spec 100v-240v which means 107 volts is OK and 132 volts is OK but if the generator is putting out poor voltage, bad frequency, and line noise - you'll have an issue with many components.
FYI.... the power company voltage is always fluctuating but frequency tends to stay close to expected values and if the transformer is good, noise should be a minimum. A generator on the other hand can be all over the place on voltage and frequency and can introduce other unwanted signals (noise) on the line and like ano pointed out, UPB commands will likely fail as well (good point ano!).
Alternatively to the UPS, there are some voltage regulators (or filters) which could possibly help but might not make sense to buy a bunch of those for every light in the house simply to make up for purchasing the wrong generator.
How is "sensitive" determined? Many devices labeled as sensitive will operate, but but power will simply degrade the duration of their lifespan. Why does one bulb work and one not - manufacturers typically produce or purchase components in bulk. In a mass of bulk components, there are some that are right on spec but most will be close. Sometimes close doesn't work sometimes exact doesn't work depending on the device. All electronics are sensitive however and bad power means a shorter lifespan.
Each LED bulb has parts - some may be "too" sensitive to operate on bad power, but you may find that others of even the same brand will operate only because all the parts are tolerant of the bad power.
Can you run your hair dryer on a generator - absolutely yes. Would you run your overpriced $12,000 flat screen on a generator - likely not if you want it to last. If I paid $50 for an LED bulb, would I purchase a $50 filter for the bulb - likely not. Would I purchase a $4000 UPS system to stabilize a few bulbs - likely not.
The choice is yours but a better generator seems to make the most sense.
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Side Note: gasoline generated more voltage because the generator speed was running slightly faster than the natural gas produced RPMs and propane runs hotter than natural gas so would also run faster. It's all about potential energy.
