should I cut down a tree
Damage to trees by lightning strikes can be quite variable. Some trees can survive for years with strike damage and some cannot, depending on the extent and severity of the damage. If you still see healthy growth in the canopy of your pine tree and want to try to save the tree, I recommend that you consult with a certified arborist. He/she can evaluate the tree for internal damage and structural integrity -- which is especially important if the tree is large and located near property. Perhaps the tree can be pruned and maintained, or it might need to be taken down if it's structurally unsound. A certified arborist will have the tools to make a determination and provide guidance on a course of action. You can find a certified arborist using the "find and arborist" section of this website from the International Society of Arboriculture. http://www.treesaregood.org/
Here is more information on lightning damage.