First, sentence B. can be restated as: In my life I have experienced enough situations involving lying to know that it is better to not lie. Around literally means to be in the vicinity of or close to. In this sentence it means that you have experienced lying many times. Enough is an adjective modifying lying. So enough lying means a sufficient amount of lying. To say so means the person feels they are an authority on this topic.

to be around something = to be present around something; to experience something to be around something a lot = to experience something a lot

This is indeed a clumsy sentence and I can see why you are confused. =) "I have been around enough lying to say so." - The narrator believes they have been exposed to many instances of people lying during their life/experiences. Therefore, they believe they have intimate knowledge on the subject. 1) ...what is the meaning of the word "around" here? - "I have been around..." This also means "I have been exposed to..." (i.e. I have been around horses my entire life. I have been exposed to horses my entire life.). You can visualize the person physically 'around' people who lie, horses, or whatever else they are encounter. 2) what is the part of speech of the word "enough" here? - 'Enough' is an adjective modifying the noun 'lying'. If the narrator had only been "around SOME lying", they would not be able "to say so". If the sentence were changed to say "I have been around lying enough...", then "enough" would be modifying "have been around". 3) how to understand the infinitive "to say so"? - 'So' refers to what was just said. In this case "I like it better this way". The explanation as to WHY they can say so is because the narrator has been around enough lying. Because it is already in infinitive form, it may be helpful to see it in past tense: Mom: "Go to your room." Kid: "Why?" Mom: "Because I said so!"