The measurement of luciferase is by luminescence, not fluorescence. There is no excitation light used in luminescence measurement, so you can measure luciferase luminescence without exciting doxorubicin fluorescence. Therefore, there will be no interfering signal from doxorubicin.

However, there is the possibility of quenching or absorbance of luciferase luminescence by doxorubicin. I don't know whether doxorubicin quenches luciferase luminescence, but you can easily test for this in vitro using purified luciferase/luciferin and doxorubicin at relevant concentrations.

Absorbance by doxorubicin of the light emitted by luciferin should not be a problem unless there is a very high concentration of doxorubicin in the medium when you make the measurement. The path length through the cell is very short, so the absorbance by the intracellular doxorubicin should be negligible.

thanks!