H&B use analysis would determine which lot is worth more. See, one could be commercial H&B use and one residential. There are countless differences between the lots that could make a difference in H&B use analysis.
I would assume zoning would be the same for the two lots if they are adjacent - the HBU as vacant would be same for either lot, but if the lot subject is on is grandfatherd in res zoning in a commercial area and the dwelling contributes more to the two lots than tear down then HBU for the assignment purpose is interim or existing - but commercial zoning would be pretty rare and if present perhaps a res license appraiser would decline the assignment.
Plain vanilla res zoning more likely the case, then it is are appraisers going to make this far more complex than needs to be - buyers are allowed to purchase a home along with a vacant lot and if lenders want to finance them, which apparently they do, appraisers, if comptent, can appraise them.
The confusion ( see marathon former thread lol ), confusion seems to be appraisers believe their assignment means appraise the vacant lot AND appraise the house and its site, and if the vacant lot can have an alternate HBU or be worth more sols separate OMG- down the rabbit hole they go. While one can, and might be due diligence to, develop an opinion of value for the escess lot, that is NOT the assignment. The assignment is develop an opinion of value for the two properties sold /conveyed as one package/assemblage ( and financed under one mortgage. ) Thus, the question becomes for HBU, as improved, does the dwelling contribute enough to the sites to be retained, aka an as is rather than demolish the dwelling and both sites /lots worth more as vacant.
In theory, if the same size, the lot of subject dwelling should be worth the same $ as vacant as the excess lot. But as a package, the contributory value of the excess lot might be less than if vacant. Which can be explained in the report as part of the analysis. That does not change the HBU of the whole property, which is the existing dwelling contributes to the sites, the second parcel does not become surplus land, it remains an excess lot parcel but serves a value in use while encumbered under one mortgage . ( value in use can be as , extra land for privacy or build amenities on or hold for investment purpose )