How significant is the lift induced drag contribution to total drag of aircraft at cruise speed? From what I've learned so far it seems to be around 10 to 15 percent of total drag. I suspect the ratio doesn't vary too much between aircraft provided they're within the same speed range. Therefore, let's focus on airliners and other high subsonic jets.
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.
These sources show 30-35% induced drag for transport aircraft at speed.
Here is a breakdown of 'typical' transport cruise drag from an analysis done for the erica tiltrotor. It shows about 35% induced drag at high speed cruise.
The Piano airframe analysis tool is generally regarded as representative of subsonic conventionally configured aircraft, and it shows 30% induced drag for the a320-200.