Possibly. Your city will have minimum setback (buffer) requirements between a lot line and a building. Not a problem if you have two homes sitting on an acre, but if you've got two homes within a stone's throw of each other, the setbacks may not offer much wiggle room. If the lot line adjustment violates a setback minimum, the city will deny it.
Look at the plat requirements under the zoning section of the municipal or county code (whichever you're in). A Surveyor will run >$1200, platting fees will be a few hundred and it'll take 1-2 months if you're quick.
To get you started, look up the setback requirements for your zone district online, and measure it out yourself to see if the lot line adjustment can comply with the requirements. Then, call city planning to make an appointment to talk with a planner and give all the info to the seller who should have done this already. Sometimes you have to do the work for them to make the deal. Consider putting it under contract pending the city's approval and recording of the replat with the assessor. Good luck, it's worth it.