Better not to use this correlations,It could give you a range and often big range. You can't use this formulated correlation to calculate and use the result.
I beleive the water content, LL, PL tells you how much pores in the soil, and the natural of the soil particles in terms of how cohesive they are. usually you can tell that a soil is pretty soft and weak if the water content is high which could imply that the soil is quite loose. and the PL, LL high could mean the plasiticity of the soil and consistance of the soil.
In our practice as a designer in a contracting company, we don't really have too much information from the client due to cost issues. we seriously just estimate the Cu based on the description in the geotechnical report, like firm, stiff, very stiff, hard, dense, very dense, highly weathered etc. of course also have a look at the SPT if they did that, which just double confirm your assumption of the soil.