Is this a weed?
Weed is a relative term. It's basically a plant where you do not want it, so I would say that yes, that plant is a weed. It is also known as a crape myrtle. My guess is that you have a crape myrtle nearby, or got rid of one in that area. Now it is sprouting from the roots. If there are no crape myrtles nearby that you desire, and none near that your neighbor likes, the best option would be a systemic herbicide such as glycophosphate. Keep in mind, if the glycophosphate herbicide touches your grass, it will kill your grass. A 2-4-D or dicamba product will harm your grass less, but I urge you to test it out on a hidden part of your lawn first. I would not apply herbicides when it is hot, wait until it is cooler to apply them.
Crape myrtle can be a tough plant to kill, and you may need repeated applications. Always read the label when applying an herbicide, and apply it according to the label instructions.
Also, here is some great information on killing out crape myrtles sprouts: