It depends on the number of tests and your needs (usually this number of cells is enough to load in 10 wells). It is best to determine the concentration of protein in cell lysates. This will give a more accurate and clean result (usually 20 micro grams per well).
The order of magnitude is generally 1-5 mg/ml protein in 200 µl lysis buffer on a 10 cm dish that typically contains 5 x 10e6 cells. The limitation to scale down protein extraction is the concentration of the extracts vs the volume of the SDS-PAGE wells to load.
In small SDS-PAGE gels you can go down to 10-15 µg if your protein is abundant enough and if your antibody is good but 20-50 µg is better. And if 10 wells are enough for the nb of conditions you have you can load 50 µl in 1.5 mm thick gels.