No matter how great of a team lead you are you will have team members that burnout. It happens. Energy and productivity are not straight lines but rather hills and loops that sometimes crash to zero.
When this happens it’s on you as the team lead to notice it and act on it quickly. If you see the mood of one of your contributors is chronically low energy pull them aside and ask them how they’re doing. When they give you their feedback, look at the whole picture. People who are badly burned out frequently don’t realize that they are. Ask them directly if they’re burned out and take their answer at face value.
Bad managers think people will claim burnout just to get more time off. Good managers realize that they hired great people, they set good, inspiring goals, and that when their contributors tell them they’re burned out they’re telling the truth.
When this happens rework the workload so burned out teammates can get a full and complete break from work without disturbance. Push goals back if needed. One week is the minimum for a teammate to recover from burnout – but two is preferred. Prepare for this person to be completely unreachable – request any work objects, passwords, and information before they leave.
This also applies to you. Leading teams is emotionally taxing and you will burnout too. If your teammates, family members, or friends suggest that you seemed burned out you likely are. Give yourself a break.