I don't know what is meant by 'software'. My assumption would be that 'software' only refers to the library included under the license (being DotNetZip) and that is doesn't extends over to my code which includes the DotNetZip library.
That's correct. The term "Software" used in the license refers to the software that license is about: DotNetZip.
If you distribute any portion of DotNetZip, you must retain all copyright, patent, trademark, and attribution notices that are present in the software (3c).
If that is the case then everything is fine as I have no issues keeping the license for DotNetZip when release this project in compiled form while having my code under its own license. If 'software' also include my code that include the DotNetZip library then that would be an issue (as it would basically act like GPL with the copyleft sense).
The latter is not the case, MS-PL is not a reciprocal license. It only requires that the software you distribute if it contains MS-PL'ed parts, must comply with the license requirements for the MS-PL'ed parts. As long as you don't give any sources from DotNetZip you do not even need to provide a copy of the license text if I read the license correctly.
I believe you've stated the differences between the Mozilla Public License and the GNU Lesser General Public License accurately, and either may suit your needs just fine, but you are skipping over the most important difference between the two licenses:
Who can make new versions?
Both the MPL (section 10) and the LGPL (section 14) include in their license grants the right to substitute the current version with a latter version, and there are no actual limitations as to what can go into those licenses. While it's highly unlikely that either the Mozilla Foundation or the Free Software Foundation will do something as crazy as, say, institute a clause that says "all contributions to this software become our property", it's not beyond the realm of possibility that one of the organizations will release a new license version that you don't like.
Which brings up another point about using a "Modified LGPL".
A modified license is not the same license!
While you have fairly amazing ability to specify your own licensing terms, and could in essence say "you can distribute this as per the GPL, but you need to put my name in your credits and pay me 1% of any revenue you generate", any time you do so you are creating a new license based on someone else's work. This means that you're NOT using the MPL or the LGPL, you're using a new "mucaho license".
What that means is that you probably won't get any help from your original license's author if you need to defend your interpretation of the license inside of a courtroom, and it's entirely possible that they might file suit to say that THEIR version should apply and not yours.
Of course, both of these are minor points. Even "license popularity" doesn't matter unless you expect your code to be directly incorporated into larger projects.
Personally, I think the MPL is a better choice if you like proprietary compatibility, or if the choice is between the actual MPL and a different license you have to manually edit based on the LGPL. Unless you have a reason not to use the MPL, go with something backed by a foundation instead of one that might leave you in a courtroom without any aid whatsoever.
Best Answer
First, a terminology correction, the word you are looking for is "proprietary", not "commercial". Open source software is commercial in every sense of the word. It is created by businesses, sold to businesses, and used by businesses. This is true in practice and was so recognized by the courts in an important legal case.
As for the license you are asking about, go to http://www.opensource.org/licenses/ms-pl.html and read the text. (Note that the license was created by Microsoft for use in software written by Microsoft - which is not known as a charity. That is commercial software.) Reading section 3.D. it is within the rights granted by the license to distribute a compiled binary including that software, however you have to abide by the terms of the software. So, for instance, you can't use the contributor's name, logo, etc for your software. (Odds are that the contributor is Microsoft.) It should be very easy to to comply with that license. But if you are in serious doubt about whether you are complying, consult with a lawyer.