There are a couple different effective ways to quickly farm your way up to 99 lives. Both involve reloading autosaves, so make sure that yours is enabled. (Check this by pressing L2 in The Time Twister.)
1. Once you reach Sphyxinator (Level 16) go ahead and start that level. After the loading screen, walk backward to spot a group of 4 boxes. One of those has a life in it - go ahead and break boxes to pick that puppy up.
2. After breaking those boxes, progress through the level as you normally would -- taking a left at the "V" at the beginning of the level. Slide, double jump and tornado spin your way to the other side of the large gap.
3. Dodge a few darts, a mummy, a monkey, press a button on the floor, and behind the checkpoint box, there will be 4 lives. Go ahead and grab those.
4. Before jumping on the platform after the checkpoint (it doesn't matter if you get the checkpoint or not) press start and exit out of the level.
5. Once your back in The Time Twister, press L2, and select the Auto Save Slot and load it by pressing X.
6. Once it's done loading, go ahead and repeat 1 through 5 until completed.
Another effective way is using the Auto Load technique on Level 3: Orient Express. It tends to be a little more challenging, but I believe it was more fun to farm out this way.
This ways also pretty self explanatory, but here's a video: