To begin with, are you sure your phone is charging correctly? I would check to make sure that your charging cord is working. Similarly, if you find that the charging cord is working, then you might be running on Performance Mode. To fix this, just simply change the mode in the battery settings to either Smart-saving or Ultra-saving (depending on your preferences). Ultimately, if this doesn't work, you may have a faulty battery. If you need help replacing the battery, check out the replacement guide on the page.
One thing that can be done to attempt to fix your connection is to check your antenna. If the signal is not consistent; then, the antenna is loose inside of the phone. If you need help taking your phone apart to see if the antenna is loose, check out the replacement guide for this device on the page. Similarly, if you cannot get any service on your phone, then your antenna may be broken, in which case it needs to be replaced.
The most likely reason that you are experiencing this lagging is because this phone can be operated using different modes. This phone has four different operating modes: Performance Mode, Balance Mode, Smart-saving Mode, and Ultra-saving Mode. Make sure that when you are playing games, you play them on Performance Mode so the game can run more smoothly. Now, be aware that Performance Mode uses the most power, so I recommend making sure that you don't play too long, because then your phone will die: or play with your phone while it's charging. Although the Performance Mode will help with the performance of game play, the lagging can be helped by simply closing programs and not letting them run in the background when you are done with them. By doing this, you will reduce the possibility of lagging on your phone.