Using potato masher, mash sliced lemons, mint, 1 cup sugar, and 1/2 cup lemon juice in large bowl until juicy, about 5 minutes. Strain lemon mixture through coarse sieve set over another large bowl, pressing masher on solids in sieve to extract some pulp and as much liquid as possible. Mix 2 cups water and remaining 1/4 cup sugar into lemon liquid and pulp in bowl. Fill pitcher with ice; pour lemonade over ice. Let stand 5 minutes. Fill 4 to 6 tall glasses with ice; add lemonade.
