Can you rearrange it to another time?

For politeness, using "we" in place of "you" = "Can we rearrange it to another time?"
This isn't a requirement however, just another way to say it
This suggests it's a decision you are making together with permission, but is more along the lines of English manners usage than anything

Sorry Mischa, I needed to reschedule the lesson onfor next Saturday evening (March 11th) from 6:30 to 7:30 that I can’t take it because I will have an activity thenbecause I need to be somewhere else.

This sounds more natural in the US.

I tried to reschedule it for another time but I failedthe software wouldn't let me.

Can you rearrangWould you please reschedule it to another time?

Sorry Mischa, I can’t take the lesson on next Saturday evening (March 11th) from 6:30 to 7:30 that I can’t take it because I will have an activity then.

When talking about activities we have in the future, we use the present tense (example: I have an appointment tomorrow). I’m not sure why, it doesn’t really make sense… but that’s how we do it :)

Can you rearrange itschedule your lesson to another time?

We often use “reschedule” when talking about rearranging meetings
I changed “it” to “your lesson” because in the last sentence, you were talking about your own activity. To make it clear that you’ve changed subjects and are talking about the lesson, I would refer directly to the lesson rather than saying “it”.