An individual lender may simply be set up to charge a set number of fees, and like a computer program, these come spitting out with no room for variation. On the other hand, you can select your lender, and there is sometimes an enormous difference in charges. So, while you may not be able to get an individual lender to reduce fees, you may be able to pay far less by shopping for a less expensive lender.
The time to shop for a lender is when you are first applying for a mortgage. It is at that point that you have the greatest leverage. If the lender charges too much, you can walk out and look elsewhere. (There's no shortage of mortgage lenders.)
On the other hand, if you wait until you're ready to close to determine that the charges are too high, you're probably out of luck. Changing lenders takes time—for a new appraisal and for a new round of qualifying. It's like starting all over again. Many sellers simply won't tolerate the wait, but will insist you close with the lender you've got or lose the deal and potentially your deposit, too. Further, it's also costly. If nothing else, you'll probably have to pay for a new credit report and appraisal. (It seems that each lender uses a different appraiser and for some reason simply can't bear to use an appraisal that you might have already paid for. The credit report only costs around $35, so it usually isn't a big deal.)
What you need to do is to very carefully read the estimate of costs that the lender gives to you. Know how many points you will have to pay as well as what all of the other fees may be. If you don't agree with a fee, speak up and tell the lender. In some cases, particularly when the market is cold and there aren't many new financings coming along, a lender may reduce or even eliminate a charge. On the other hand, if the market is hot and there are people waiting in line to get financing, don't expect the lender to budge.
Note: we're talking primarily about charges in addition to the interest rate and the points on the mortgage. These are usually (but not always) competitive. You can shop around for these simply by calling up different lenders or mortgage brokers and asking what are the best points and rate you can get. Also, rate and points are often posted in big, bold letters on the documents you will be asked to sign. It's the other charges that are located in the fine print that you usually want to watch out for.