Here is how to maintain lean burn while shifting in a Honda Insight, this may work on other lean burn engine but no testing has been done. So here is what I know, you must have a calpod/card/clutch switch. if you have the clutch switch "on" as in the car thinks the clutch is pushed in, while keeping your foot on the gas pedal even just slightly you can change gears up or down and still retain lean burn. I use it to climb hills by downshifting to 3rd or 4th or speeding up by shifting to 5th.
Here is the break down
you need:
1st. clutch/calpod switch engaged.
2nd. you need to already be in lean burn.
3. keep your foot on the gas.
4. shift quickly as to not over-rev.
5. Bam your still in lean burn changing gears!
Here is a quick youtube video showing me maintaining lean burn while shifting from 3-4-5 and 5-4-3.