I don't do bromoil prints at all, but the 'substance' that forms tone in a lith print is different, especially the highlights. When you bleach a lith print to tone it, the highlights often don't come back at all, unless there is some silver converted in that area. I believe that some of the highlights form due to an oxidation process, so I don't know how you'd get your highlights to ink after you bleach it.
As I understand it, you want your matrix to be about 1/2 stop overexposed in the enlarger. When you do that with a lith print, you obviously lower the contrast. But you could potentially overexpose the print to lower the contrast and then overdevelop it in the chemistry. That would give you normal blacks while getting a heavier tone in the highlights and midtones. That might give you enough converted silver in the highlights to make a bromoil matrix from it.
Just my 32 cents based on toning lith prints (using either copper sulfate or potferri). I think bromoil employs copper sulfate bleach, but I'm not sure. You're going to have to fill in those blanks here.