Releasing a proprietary program under the GPL

[sctkell]

Hi,

I'm trying to learn about and understand the GPL and I hope I can
present this question in a coherent manner.

Let's say I'm the copyright holder to a proprietary program P.  I want
to change the license for P to use the GPL.  However P is heavily
dependent on a 3rd party proprietary library L.  The license for L
does not permit the redistribution of L's source, and you can only
redistribute L's binaries if you have a "development license" for L.
Also, L does not fit the definition for a "system library".

At first I thought no problem - GPLv2 and v3 have a provision for the
copyright holder to give permission to link P with GPL-incompatible
libraries lilke L.

However, let's say I want to integrate a GPL covered library G into my
new GPL program P.  However, unlike P, the license for G does NOT have
a provision saying it's okay to link G with L.  So could P link with G
and L and be redistributed like that?

Thanks!
Scott