I planted two types of morning glories and one Moo flower around a dead tree in our front yard. I already know that plants prefer to climb living things but I figured they would make this old tree look pretty.

My question is this.

How do I get my plants to stop growing on the LAWN vs. The TREE.

And if I mow my lawn ( and mow the vines on it in the process) will that kill the plant or will it regrow?

Which type of morning glories?

And

they are probably going to keep growing toward the sun, they are not wanting to grow on the grass, just that under the tree there is less sun and they grow/bloom toward the sun. you can try some wire/trellis and tie them up to it as they grow.

Morning glories will twine around any support you give them, but they will not spontaneously jump up into your tree without help. You need to give them some sticks or strings to lead them up into the tree where you want them. Then they can twine around the thinner branches.

If you mow them, they will probably re-grow, but never get tall enough to climb into the tree.