I got inspiration for this question from this paradoxical question: Can a Green Lantern be made of constructs?
From what I can remember from TV cartoons and Green Lantern (2011) movie, green lanterns construct only non-living objects: Guns, swords, shields, cars, fighter jets etc.
But, in the movie, Hal Jordan was told that "Only your imagination is the limit." Does that mean I can construct herds of T-Rex and have them autonomously charge at enemies? Can I construct an army of Darth Vaders who could intelligently think to crush the enemy?