Does anybody know where I can find out how many lines the bus system in Tehran has?

I guess no one knows :D
there are a lot though

yeah, The only things I could find were the trolley buses and BRT, which totals around 8 lines

Gitashenasi (http://www.gitashenasi.com) used to publish a map of Tehran with public transport lines. Most likely this (http://www.gitashenasi.com/shop/product_info.php?cPath=38&products_id=870) is the product. It might be obsolete in some part but it gives a pretty good orientation.