Why did you even agree to go on a date if the thought of spending money on someone else, is in and of itself, so off putting to you?
I would suggest you pursue friendships instead of dates to address your loneliness. They don't require you to spend money on others, and they don't require the same level of commitment. With friendships you'll still have plenty of alone time to spend as you wish.
Unless of course you didn't mean general loneliness, and meant specifically the romantic kind....
Then I would say, you have a choice to make. Choose to accept that dating requires time and money, or choose to deal with the loneliness.
Free will and all that
Ps. I concur, it would be rude to cancel, one date won't kill you.