Is it Ho-oh?

The victor thrice, approacheth hence,
The door hath been blocked without sense.

In order to ascend the stairs into Tin Tower, you must have won against the Wise Trio, captured each of the Legendary Dogs, and defeated the Elite Four. Until all three of those steps have been accomplished, there will be a monk guarding the staircase; once all the steps have been fulfilled, the staircase magically appears out of thin air.

Façade awaits you, keyholder.

The façade in question might refer to the Rainbow, which looks like it's there but it really isn't (all 'it' is is a sort of optical illusion); the 'key' would be the RAinbow Wing.

Beware thy future batt’ling err;

Again, this one eludes me...perhaps that it's a bad idea to try and capture it with the Master Ball?

Seek wisdom now, or fate is doom.

This could refer to the Wise Trio that you must defeat in order to access the Tower, and the fact that the tower is run by monks (a group of people noted for wisdom).

Light sheds as growth avoids its bloom.

The shed light in this case is easy: a rainbow forms in the path of wherever Ho-oh flies. I'm not sure of what would sort of 'growth' would hide from a rainbow, however.