Although pure speculation, the word MAY come from the candy Lolipop. Someone (or more than one specific person) may have used this as an extended version of lol as some people do and rewrote it in a funnier way.
The word Lawlipap is speculated to have its origins in the online computer-game (MMORPG) World of Warcraft. Some European World of Warcraft players claim that it has its origins on the in-game server “Bronzebeard” although there is no proof of this.
“Feel hard pwned you noob? Lawlipap!”
S: “You se that Warrior over there? HE USES FREAKING CLOTH ARMOR!”
A: “LAWLIPAP!!! He must be da noob of the year!”