Hi Magroud!
For the main question in your post, let's approach it from a PMI perspective -- in other words, let's connect the question to the PMBOK (and other study guides), and refrain from the "what I'd do in the real-world" perspective.
The most important concept to understand for this question is that the PMBOK emphasizes that litigation should be the LAST thing you try when attempting to resolve disputes, and alternative dispute resolution (ADR) techniques should be first attempted.
The question tries to throw you off with the following information: "Having reviewed the situation with the supplier, you realize that you have taken the discussion as far as you can without legal advice. You call your lawyer, and after reviewing all the available documents, the lawyer suggests going into litigation." So, instead of looking at the information which is presented (and is misleading), let's look at what's NOT there: Has the question indicated anywhere that mediation or arbitration (ADR techniques) has been attempted? Nope! From the question, it seems that you have only had one-on-one discussions with the supplier and nothing else.
So before jumping into litigation, ADR is the way to go. Also, this is a question of determining the BEST correct answer, not just the correct answer. Perhaps deducting the penalty is the correct thing to do, but PMI would suggest first using an Alternate Dispute Technique to make that decision.
As for your last question about whether or not to consider the lawyer as a stakeholder, the answer is YES! Note that the definition of a stakeholder is an individual, group, or organization who may affect, be affected by or perceive itself to be affected by a decision, activity, or outcome of a project. Technically, the mailman delivering a project's contract could affect the project, and your next-door neighbor could perceive that they could be affected by the project -- so almost anyone can be considered a stakeholder! My examples are a bit of a stretch, but correct according to the definition. So, yes, a lawyer used on a project could easily be considered a stakeholder in it.
Let me know if you need any other clarifications!