All 240 stars are mine! There is now just one galaxy left, the Grandmaster. On my first attempt, it gobbled up 30 lives like my kids eat ice cream. It wasn't pretty. Before I tackle it again, I'm going to need a lot o lives. What's the best way to get as many extra lives as possible in a short amount of time?
On Starship Mario (the hub world), near the right "ear" of the starship, there is a pipe with two Lumas in it.
The first offers you one chance cube for 30 star bits. The other offers you 5 chance cubes for 100 coins.
Each of these chance cubes has 1 star bit, 1-up, 3 1-up, and 5 1-up sides.
Needless to say, you can get anywhere from 0-25 1-ups for 100 coins.
Note: I'm not exactly sure when each of these Lumas appear, but neither are present at the beginning of the game. However, the requirements for reaching Grand Master Galaxy should cause both to appear.
During an unrelated search, I came across this page of cheats/hints/tips/tricks which links to a video showing how to get infinite lives in the Supermassive Galaxy, the first galaxy in World 4.
After the first checkpoint, take the launch start to the disc-shaped planet with three giant Koopa Troopas. Long jump onto the back of a turtle. (Avoid the drill; you can't do a long jump with it. If you happen to accidentally pick it up, run into one of the Koopas to lose it.) Once on the back of a Koopa, Mario will start to bounce. After eight bounces, he'll start to get an extra life for each bounce. You'll have to do a little steering with the control stick to stay on. In a couple minutes, you'll amass the maximum 99 lives.