In a thoroughly cleaned large gallon-size glass container, fill cold water leaving 2 inches of space at the top.
Open all of the tea bags and put them in the container with the strings hanging on the outside edge (of the container).
With clean kitchen scissors (used for food only) cut the cheesecloth into a piece about 15 inches long. Put the cut lemons and pieces of mint on the cheesecloth.
Pull up the edges of the cheesecloth and gather it around the lemons and mint so they are in a pouch; then tie the string around the gathered part to keep the pouch tightly tied. An option is to cut off the tail of the cheese cloth right above where the knot is tied; this way the cheese cloth won’t hang out of the container of tea.
Put the cheesecloth pouch with the lemon and mint into the jug of tea. Let the string hang out on the outside of the container.
Put a lid on the container and let the container sit in the refrigerator overnight for at least 6 hours. Then remove and discard the tea bags and the cheesecloth pouch. It's best to have a plate handy to put the tea bags and cheesecloth bag into after removing them from the container because they'll have residual liquid on them.