I've had many apratsments on leases, how do you get a cat to walk on
one?  

Use one of those H type halters. I understand that they work the best.
Start by laying the halter on the floor an letting the kitten explore
it . Then place the halter on the kitten give it some treats as you do
this.
Do this once or twice a day for a week or so.
This gets the kitten associated with good things with the halter.
Then let the kitten walk around with the halter on for a few hours.
(If the kitten, or cat, sulks or runs and hides,  then I would
discontinue the halter thing and try later)

Praise the kitten and give it some treats.
Then put the halter on and attach the leash.
Let it walk around SUPERVISED.
This gets it used to having the feel of the leash.
As always rewards and praises are in order.
Then take the kitten outside HOLDING IT with the halter on.
Give it treats when you get back inside.
Do this several times a week
Then carry the kitten outside with the halter and leash attached
HOLDING IT.
repeat.
Then take the kitten outside with the halter and leash attached and
let it explore.
If it does not want to explore then just let it do "it's thing".
Some cats like being on leashes, some don't.
It depends upon the cat.

This is how I tried it on my cat.
For What It Is Worth; he had already been outside W/O a leash and
harness, so he did not take too kindly to the restriction.
I just wanted to walk him into Pet Smart when they had puppy training
day!

If the Kitten walks on the lease before the term expires, then they'll
be responsible for all rent until the lease expires, same as if you
walked on a lease.  Why?