How many lumens (lm) should a front light have? I need a front bike light for pretty quick night riding on roads beside the town. I found one that has 120lm, 30lux, and 92m shining distance.

Is it enough? What parameters should a good front light have?
A front light needs to have both enough lumens (brightness) and have those lumens pointed in the right places - dictated by the reflector and lens. It also needs a battery (presuming its not dynamo powered) to last the length of the ride with some reserves. Addition things to consider are ease of install and removal from bike and mounting location, and battery size ( do you need to charge after every ride, or once a week?) . 

More Brightness is easy to cheap to achieve and easy to sell (Mines bigger than yours), and very easy ti lie about "6000lumen". Reflector and lens is design is hard to achieve and hard to sell "Its not the size, its what you do with it that counts" 

There are plenty of cheap Chinese lights on ebay that will do a good enough job for under $50, closer to $20 - they work on the "Bigger is better". For a better light in every way, you need to move away from these to a brand name light costing much more to something that has some brains behind the design. 

My budget dictates cheap Chinese lights and accepting the poor light distribution  My $25 lights claim 1200 lumen, probably have 600 and its all pointing to a high intensity spot with very little out to the sides.The battery is claimed at 4400mAH, I have measured it at  2000mAH, but do get the claimed 2 hours on high.

As already suggested, refer to the BikeLightDatabase,