You're SO lucky that it's only 150 dollars(: Where I live leasing is almost 700 a month.
Anyways, you could probably get some cash doing chores around the barn and such. You know, cleaning stalls, stables, horses. Try making a deal with your parents, too. You know, use good grades or all the chorse you do to your advantage. Depends on how much more money you need, tho. Maybe negotiate a lower price with the owner of the horse you want to lease. Don't feel bad about kissing up in this case - get him/her on your good side.
As far as grooming goes, if you are thinking about leasing a horse, you probably already know how to do it for the most part, right??
So yeah, good luck getting the money. Leasing is a lot of fun, and SO much cheaper than owning a horse.
BTW. By not having your license, do you mean drivers or working license?
JW. Are you interested in showing and/or owning horses in the future?