eslHQ - rely on VS. lean on

The first is OK but the two sentences have different meanings.

Rely on

If someone or something can be relied on, it really means that their/its behaviour is predictable. So ...

You can rely on David to help.
but also
You can rely on David to be late.

ie David's willingness to help or his lateness is fully predictable and you can be sure it will happen. But it may be something positive or negative.

When rely on is used without the infinitive ...
You can always rely on David.
it generally has a positive meaning - David is predictably trustworthy/helpful/will always do what he's supposed to etc (the exact meaning depends on context). So :
You can rely on me in this situation = You can be sure I will do what is necessary in this situation

Lean on

lean on literally means "put your weight on" :
We couldn't shut the door even though three of us leant on it.
The old man leant heavily on his son's arm as they walked along.

The second example above shows that it has the idea of someone supporting another person, and metaphorically it can be extended to express psychological support. I found these sentences in the Cobuild Concordancer :
...one of life's great comforts: being able to lean on someone for support and strength
I've got the rest of the school to lean on. Heads don't have that kind of support
So your sentence You can lean on me in this situation would mean I will support you in this situation - slightly different from the meaning of You can rely on me.

This means that in your second example lean on is unlikely - your "destiny" can't support you. You may however consider it predictable and something that you can rely on to happen :

I had no idea how I would achieve my aim of becoming an astronaut, but I knew in my heart that it was my destiny to do so, and that I could rely on my destiny to find the right path .

Notice that lean on has a second metaphorical meaning, however - to put psychological pressure on someone :

John didn't want to work Saturdays, but the boss leant on him until he agreed.

and from the Concordancer :
... new detente with the United States, they might lean on Syria to give concessions
Attali rang the head of Elf to see if he could lean on the head of Enterprise to give up his ...