Protocol that works on tissue often works on cell lysate. Try to adjust protein concentration of your lysate, to that of the tissue homogenate, as described.
Take a look at the reference below. It describes the protocol for enzymatic recycling measurement of total GSH and GSSG levels from different sources, including cells in culture. We use this protocol frequently, but for animal tissues.
Irfan Rahman, Aruna Kode & Saibal K Biswas. 2006 .Assay for quantitative determination of glutathione and glutathione disulfide levels using enzymatic recycling method. Nature Protocols 1: 3159–3165. 10.1038/nprot.2006.378