Thank you for the all replies. I dug around the roots a few days ago and found that the soil was somewhat moist but dryer than expected given the rain we have received the past 2 weeks. The leaves started turning brown a few days after we got rain, and the lawn is thriving without signs of drought stress. It would be a little surprising if the issue is drought damage in April, but since this is the best explanation I have at this time, I will give the shrub more water. I think herbicide from a source like weed and feed is very unlikely since there are only shrubs and no grass in the immediate area. Thank you, cpp gardener, for suggesting that this plant is Ternstroemia -- that looks like the correct identification for this shrub.
If anybody has any other thoughts or possible explanations for the brown leaves, please let me know. Thanks again for your help!