Most of the dreamworld ILs can be done in your first attempt (starting the level from the menu) as it's already good enough for getting a fast time or there are no cycles. Nevertheless, there are a few ILs with cycles where you have to wait. Well, "waiting" and "speedrun" is a contradiction. So, how do we eliminate "waiting"?
There we need to know how cycles actually work: They move as long as you don't reach the end of the level. When you're at the end of the level showing up the leaderboard to see your reached time, the cycles are paused. When you press "Restart", the level restarts but the cycles do not reset! They continue from their position where they stopped. How does this information help?
Let's investigate us this in "That's a Loot of Fruit". The first lap is horrible. You have to wait for the first kiwi as well as for the "kiwi-stair". Time waste of 20 seconds.
So, we gonna find out the cycle for the first kiwi.
Starting from the arrowhead to the arrowhead again, this kiwi cycle takes 16 seconds which means "Every 16 seconds this kiwi is at the arrowhead position". It's getting better: From your starting point, you can reach this kiwi instantly (no waiting anymore that the kiwi comes to you, you come to the kiwi).
And how does this help for the whole attempt? Of course, this trick is only helpful for your 2nd lap but you need to find out when you finish your 1st lap. This is some inevitable "trial and error". For this level, I got the time for you:
In order to have a perfect 2nd lap, you need to finish your first lap in around 2m02s (for PS2). You restart the level and can use the kiwi instantly. Why is this "perfect"? Well, accidentally the "kiwi-stair" is also instantly reachable but its cycle time is different, 13 seconds for curious people.
So, I think you know what happens when you finish your first lap in 2m18s? Yes, first kiwi is still fine but the kiwi-stair ruins your attempt.
When do both cycles harmonize again? It's after 1m05s +/- 3 seconds (for PS2). For careful readers, it's almost the time for the kiwi cycle multiplied by 4. So you get 3m07s, 4m12s, 5m17s,...
Conclusion: Sadly, none of those times improves the section after the kiwi beginning. The cantelopes are always in the same position like when you start at 2m02s.
So, it's enough to find out the lowest time to end the 1st lap to get a perfect 2nd lap.
This thread is also interesting for Veggie Vault and other ILs whose 1st lap isn't satisfying.