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What you are describing sounds like each dataset has distinct coordinate systems (probably based on different projections). Do you know that coordinates systems of the "USGS data" and the "LIDAR data"? It is rarely the case that a simple shift or correction factor will transform from one coordinate system to another. You may know this stuff already and I am not understanding your question. If not, here are some questions to get you started:
1) Are the data coordinates in units of US Survey Feet, International Feet, Meters, Decimal Degrees, Degree Minutes Seconds, or something else?
2) Did you receive metadata with the other data?
3) What are the data coordinate systems?
I suggest checking out the following sites:
National Geodetic Survey (NGS): Remote Sensing Division
University of Washington: Introduction to Geographic Information Systems in Forest Resources
University of Colorado: Coordinate Systems Overview
Colorado State University: State Plane Coordinate System
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tsgrue: site engineering, stormwater
management, landscape design, ecosystem
rehabilitation, mathematical simulation