These are different uses of the word 'cause'.
In (1), (which is NOT a sentence), the word 'cause' means 'for the sake of' or, 'for the principle of'. It is important to
disregard the strict letter of the law, so that true justice should be done. Sometimes, if we were to follow 'the strict letter of the law' as written, justice would not be done. For example, it might be that if we (Britain) followed the law 'to its letter', someone might be deported to a country known for torturing its political opponents. So, it is important not to adhere to the law too dogmatically, in order for fairness or humanity to result.
Here is another example of this 'cause of': He gave up his life for the cause of democracy. Democracy is NOT the result of the sacrifice of his life. True justice is NOT the result of disregarding the strict letter of the law. In (1) 'cause of' means the aim, or the principle under which an action is carried out.
In (2), cause means 'that which produces an effect'. The effect of smoking is heart disease. We say there is a causal relationship between smoking and heart disease.
In (3), there is no causal relationship since this is an opinion, not a fact. Here 'cause' means 'reason for'. It means, 'I do not believe that you have reason for complaint'.
I hope this gives you cause for thought !
