I have a few suggestions to tidy up your poem. One way is to make more stanzas like so:

WALKING OUT

I wonder if I am now coming to the end
With only just a little money left to spend
To pay the ferryman, who will comprehend
Across the river Lethe, memories destroyed (.)

No finish line, just one last step into the void
It is just fate, so no need to ever get annoyed
Leaving a lost life that’s not worthy to extend
Into the depths of Hades, ready to descend
None there to welcome me, nor to befriend

I may look back, but there is nothing to see
It’s all about the future that’s waiting for me
Being the best lost soul that I could ever be
Yet before I go, there is one thing left to do
A final challenge, and I must see it through(.)

Only then can I turn around to bid Adieu
I don’t want sadness or misplaced sympathy
But maybe play again my favourite melody is favorite misspelled?
As I walk out into darkness, I shall be free(.)

I really enjoyed this poem!
*hugs, Cat