I am really confused: how can you draw infintie things? An infinite number of anything would require infinite resources. Not just infinite pencils, but also infinite time. So it's just impossible to calculate infinite field lines.
Nevertheless, physicists like to use infinite for everything; but even if you could calculate them, if you drew all of them, you'd fill the whole paper sheet/ screen, because there are field lines in absolutely all points in space, so field liens would fill up the tiniest hole of blank paper. You'd just see a black surface. What's the point?
Absolutely nothing. We just draw some of them, enough to get the idea of how the system is working, and then we step into the important things.