You need to speak to your real estate attorney and get their definition of a pencil appraisal and their opinion on the matter. Lenders typically conduct their own appraisal on the home, after you make an offer and sign a contract for the purchase of the home. You pay for this appraisal, not the seller. The lender will choose their own approved appraiser. This appraiser does not work for you. You can not tell them you desire a certain price.
Is this your first time buying in Manhattan? Are you working with a Realtor, at all? They can walk you through the process of buying in Manhattan and provide you estimates on closing costs.
Your mortgage broker should be able to advise you on how much of a mortgage you can afford without having to get an appraisal on the apartment. You goal should be to buy an apartment you can afford. Speak to a few mortgage professionals. If you need any referrals for lenders, email me. I would be happy to give them to you. Also, Coldwell Banker has a Buyer's Guide to Buying in Manhattan. I can forward this to you via email, also.