The fluorescence depletion spectroscopy (FDS) was used to study the structure of 11 La I lines in the visible green-red region 579.5-645.8 nm. A discharge tube with hollow cathode was the source of free La atoms. The measurements were carried out for two mutually perpendicular states of linear polarization of the laser light. The spectra were recorded in the presence of a magnetic field of about 800G. We determined Landé gJ factors for 7 levels, we improved the precision of the hyperfine structure (hfs) data for 6 even parity levels and we reanalyzed gJ data for several other levels of La I.