Personally I would rather say "vigorous trees" because of the sprouts and branches.

"Trees are full of vigor" expresses a general idea about all trees. Trees are full of vigor, rocks are not. It is correct. It is a slightly unusual word to use, but I can imagine saying it. "The trees are lively" is wrong. Lively implies rapid action or motion. "Vigor" expresses the idea of being full of life force, but not necessarily rapid movement. There is a phrase, "Hybrid vigor," which means that hybrid plants are often stronger, healthier, faster growing, and hardier than purebred plants. "Hardy" is used to describe plants that are capable of thriving almost any condition. "I wouldn't choose that tree for your backyard, it doesn't do very well in our climate unless it is in just the right location. I would suggest this other tree, it's very hardy and will grow almost anywhere."

This won't really help you but I can't resist quoting it. You can see how one American writer describes a vigorous tree! “There's a tree that grows in Brooklyn. Some people call it the Tree of Heaven. No matter where its seed falls, it makes a tree which struggles to reach the sky. It grows in boarded-up lots and out of neglected rubbish heaps. It grows up out of cellar gratings. It is the only tree that grows out of cement. It grows lushly... survives without sun, water, and seemingly without earth. It would be considered beautiful except that there are too many of it.”--Betty Smith, "A Tree Grows in Brooklyn" The tree being described is Ailanthus altissima, a Chinese tree that became an invasive species in the U.S.