Can we compare risks of lotteries? I understand the concepts of risk-aversion, risk neutrality and risk-attraction. I wonder if it possible to compare risks between two lotteries without giving the utility function. For instance,  Let X = (10, 20, 30) and consider two lotteries L1 = (1/3, 1/3, 1/3) and L2 = (5/12,1/6,5/12). Can we say that one lottery is riskier than the other?
You might be looking for the concept of stochastic dominance:

Roughly speaking, first order stochastic dominance of distribution A over distribution B, means that for every possible outcome gamble A pays out weakly more and in at least one state it pays out strictly more. Roughly speaking, second order stochastic dominance means that distribution A has the same risk as distribution B but a higher mean (but not necessarily weakly-higher in every state of the world. Alternatively, you preserve the mean of distribution B and you "scrunch" the probability mass to create distribution A. "All risk-averse expected-utility maximizers (that is, those with increasing and concave utility functions) prefer a second-order stochastically dominant gamble to a dominated one." 

The seminal paper is Rules for Ordering Uncertain Prospects (Hadar and Russell (1969))