Hills, a partner at Mayo Wynne Baxter solicitors, will undertake the feat in September and is aiming to raise £4,000 for the organisation, which provides support for bereaved children.
He must secure a minimum of £2,900 by June 24.
On his JustGiving page Hills said: “Trauma and bereavement in childhood can take many shapes and forms but the effects can be lifelong and life changing, sometimes only appearing many years later with devastating effect.
“Winston’s Wish is making a difference now. And in a small way so can I - and so can you. To help these children grow in to the happy and secure adults of the future.
“Yes, it’s an adventure. But an adventure that can make a difference. So please help me make a difference, dig deep and give what you can.”
If you would like to donate to Lee please visit his JustGiving page.