How significant is the lift induced drag contribution to total drag of aircraft at cruise speed?
According to an article on leehamnews.com, the drag breakdown for an A320 at FL 370 and Mach 0.78 is:


  The 7,900 lbf of drag is composed of 4,700 lbf of Parasitic drag or drag independent of lift and 3,200 lbf of Induced drag or drag caused by lift.


With the induced drag being ~40% of the total drag.



Related:


Why would maximum fly-time (endurance) not coincide with max L/D operating point?
Why is the thrust/drag increase much lower at a lower FL with weight the only variable?