Lubricant is a component which is useful to reduce some Conflict between surface. You have to chose one of the best lubricant for your bike and good lubricant is contain with this characteristic. Low freezing point, thermal Vasilis and etc.
Well as long as you are maintaining and replacing your lubricants periodically, there is no need for synthetic base, but if you use it a race bike it would be great investment to use synthetic based.
I usually order Repsol oil from 4 Wheel Online. For my daily driven bike, I only use mineral grade and change the oil and filter every 5000kms, but with my race bike, i only use fully synthetic oil and replace the oil and filter every 3000kms.