Playing videos that is higher than the device's display resolution will not damage the phone. As long as the phone supports the video file, it will play. About lag, most smartphones nowdays should play 1080p videos, doesn't really take that much processing power. If you are taking about very high resolutions (something like 4k videos), or codecs that requires high CPU processing power (something like h265 codec, which isn't widely used yet, still new), phones will have a hard time playing the video, which will cause lag because phone's hardware today aren't enough for that (for now, as technology always advances).