Laemmli buffer contains bromophenol blue dye, if you use it for protein isolation, you cannot measure the whole lysate protein concentration using regular protein concentration measurement methods.
On another hand, you need to disintegrate the plasma membrane (and/or cell wall), so standard lysis buffer should be used. After preparation of whole whole lysate, Laemmli buffer is used for sample preparation for several reasons:
Bromophenol blue breaks the disulphide bonds, if present.
SDS linearizes protein to its primary structure and incorporate equivalent negative charge
Glycerol provides viscosity
Laemmli buffer can be used as an elution buffer in some immunoprecipitation methods where protein concentration measurement is not needed.
I used 2x Laemmli buffer. 80 microliter for 3 million cells. Vortexed and bolied for 10 min at 100 C. Checked protein concentration in nano drop and I got the concentration in mg/ml.
Correction: It is beta-mercaptoethanol that breaks disulfide bonds in Laemmli sample buffer, not bromophenol blue. Bromophenol blue is just a tracking dye for the electrophoresis. You can leave out the dye from the Laemmli sample buffer if you want to make it yourself, although that makes it difficult to tell when to stop the electrophoresis.
I think the measurement of protein concentration by UV absorbance using a Nanodrop spectrophotometer may be inaccurate because of the absorbance of the dye. Leaving out the dye should help reduce this problem.
If the protein concentration is not important for your experiment, it is OK. Or you need to prepare cell lysates by other buffer and add Laemmli Buffer 2x after detecting protein concentration.