A living trust is cheaper than a will and probate. Sometimes, Sometimes not. It depends on your situation. If the trust and the necessary transfer documents do not cost a great deal more than a will, and probate is in fact avoided, it can be cheaper. This needs to be analyzed very carefully.
Lawyers charge a percentage of the estate for probate.
This is rarely the case anymore. I know of no lawyers that currently charge a percentage. If you ever find yourself in the office on one that does you should be very leery. Only after conferring with a competent attorney that you have hired can you determine if you want a will or a trust. There is no substitute for an attorney who has been hired to give you his best advice.