I'm aware that the word "sticked" exists, Cristi, but I am recommending that you used "stuck" if you wish your English to sound natural. I never hear anyone use "sticked," and my computer even underlines it as incorrect. I am informing you that STUCK is the best word to use.
So lift consists of three sides, I suppose to mean it gets sticked on any of the three sides, but I was also concerned if I use "on", it can imply the lift top. Appreciate if you could shed some light
"Lift consists of three sides." Why are you not using "the"? What do you mean by "I suppose to mean"? "On" can be used for sticking something on the exterior; it doesn't. If an English speaker wanted to speaking of sticking something on top of something else, he would use "on top of."