Len, choose tetrahedral unless you are certain the LUT represents a straight line, in which case linear may work. Nearest requires the least amount of calculation but also offers the poorest (i.e., least precise) results. Linear requires the medium amount of calculation and the result should be OK as long as the LUT represents a straight line. Tetrahedral requires the most calculation, but it can handle curved lines.
In reality, most modern computers are fast enough to handle the amount of calculation needed by tetrahedral without a noticeable difference in processing times and if it is a LUT you have downloaded from someone else you will often not know whether it represents a straight line or a curve, so in most cases it is best to pick tetrahedral.