Super Mario Bros. 2, known as Super Mario USA in Japan, is a curiosity in the mainline Mario series. Nintendo of America thought that the Japanese version of Super Mario Bros. 2 would not be seen as a big enough advance, so asked them to create a new version, for the Western market. The popular Famicom Disk System game Doki Doki Panic was ported to the cartridge format with minor changes, mostly to fit the Mario license. Many of the holdovers from the original game have since been incorporated into the Mario series.
In response to a question posed on the forums, forum member 'Flylighter' determined that the theoretical maximum number of lives gainable as 557,396,329,246,882,030,426. The linked thread includes instructions. His estimate of how long this would take to achieve is 2,777,841,450,626,986,826,572 seconds, or 'about 88,026,363,867,855 years and 5 months'.
In more concrete terms it was put 'If you wanted to get the maximum number of lives, and then blow them all at a rate of 1 per second, it would take you over 102 trillion years.'