I posit that N != N. We don't know what N is but we can safely say that N = N without knowing what it is. That's a severe over simplification of it but I hope you get my point, that by analyzing the bounds of what might be possible one could narrow the range of possible values. Pi as an example, we don't know what it is exactly but if someone narrowed it to between 3.14 and 3.15 that'd be good enough to work with depending on the application. This particular application doesn't need to be 100% accurate - just like all population models we currently use.
Since N ~= L in this case the bounds of L are important. Fermi's argument can pose a reasonable upper limit of 1,000,000 million. The lower bound could be argued to be proportional to our ability to scan the entire sky for these signals. SETI in 36 years has scanned 0.006% of the radio frequency in 2% of the sky - that's a LONG time before we can scan the sky just for radio frequencies and doesn't include signals that might be obscured/blocked by their position in relation to us in the milky way. One could argue, barring some major change in our ability to scan, that the lower bound of L might be as high or higher than 5,000 (arbitrary number but it should be possible to figure out) as anything lower we'd have a near zero chance of detecting anyway.
In the end it might be something completely different, but until the knowledge exists supposition to narrow those bounds as much as possible is all one can do. We've narrowed it from 0 to infinity to 5,000 to 1,000,000 in this conversation... imagine what proper scientists/mathematicians can do?