First thing I would do is have the lender request a "redetermination of value", which it sounds like you have already done. I would also request that the lender ask the appraiser to "show their work" as to how they determined the contributory value of the finished lower level. Because you are not the lender's customer, you may have to have the buyer make these requests.
Please keep in mind that for business reasons, I do not complete residential appraisals for secondary market transactions. However, I do many odd and higher-end residential appraisals, and I do encounter situations similar to yours where the lower level is finished and may include direct exterior ingress and egress. Also, due to heavy frost, local code requires that foundations be at least 48" deep, so over the years, most construction digs down another 48" to provide a full-height basement. Probably 75% of the homes in this area have a basement, with 20% having a crawl space and maybe 5% being built on a slab. Most homes are built on a slab because of a high-water table, such as being near an inland lake, with the foundation still being built below the frost line and then backfilled.
My usual approach is to review the Marshall & Swift Construction Cost Guide for single-family dwellings. Then, based on the type and quality of construction, I will estimate the cost of construction using the above-grade finishes as my guide, and then look at the estimated cost for constructing and finishing a basement based on the finishes present. Presently, the per square foot cost for a dwelling featuring good quality construction above grade with similar finishes below grade indicates the below grade cost to be approximately 82% of the above grade costs. For comparison purposes, the cost of an unfinished basement is approximately 18% of good-quality above-grade costs. I will then consider making adjustments for things like interior and exterior ingress and egress, functionality, whether it is an over improvement compared to the market, the results of my comparable search, etc.
This may not be the perfect methodology, but the beginning assumption is based on industry-reported construction costs with some tweaks being made for more localized market-supported adjustments. The better and more supportive the localized information is, the more I will rely on that when considering the level of my adjustments.