Why did Mr. Lorry try to convince Lucie that he was't a friend of her father?
When he first told her the real reason behind their going to paris in the first book.
He said: "I speak miss of twenty years. He married an english lady and I was one of the trustees. In a similar way I am, or I have been, trustee of one kind or other for scores of our customers. These are mere business relations, Miss; there is no friendship in them, no particular interest, nothing like sentiment......"
You have asked a very interesting question, but in my opinion it is slightly misguided. Mr. Lorry isn´t trying to say he is no friend of Dr. Manette - rather he is reflecting the official Tellson´s Bank position, which he tries to escape from during the rest of the book.
This quote you have given comes in Chapter 4 of the first book of this novel, and is part of the conversation Mr. Lorry has with Lucie where he tells her the real reason that she has been called to France - because her father has been released but in a very pitiful condition. You will want to look how Mr. Lorry presents himself and the information.
What highlights Mr. Lorry in this conversation is his attempted avoidance of any kind of emotion - both from himself and Lucie. He says:
"Miss Manette, I am a man of business. I have a business charge to acquit myself of. In your reception of it, don´t heed me any more than if I was a speaking machine - truly, I am not much else. I will, with your leave, relate to you , miss, the story of one of our customers."
Notice here that Mr. Lorry asks Lucie to hear him as if he were a "speaking machine" - he sees himself as dehumanised and stripped of emotion in his role as Tellson´s Bank´s representative. Just a couple of paragraphs on, he repeats himself, again stressing that through his work at Tellson´s Bank he deals with many clients and therefore: "I have no feelings; I am a mere machine." He continues to stress this, later describing his life and job in the following way:
"I pass my whole life, miss, in turning an immense pecuniary Mangle."
Mr. Lorry obviously views his life as being solely focussed on his work, this "pecuniary Mangle" that he "turns" through his job at Tellson´s Bank. This is why he cannot form any emotional attachments and is just a "machine". As the conversation develops he continues to stress this with his frequent repetition of " - a matter of business" every time Lucie gets slightly emotional. Of course, his future behaviour belies his insistence, as he becomes very attached to Lucie and her father and their family.
So, Mr. Lorry isn´t saying he isn´t a friend to Dr. Manette - he is just saying it is a "matter of business." One of the key themes of the novel is imprisonment, and we as readers come to see that Mr. Lorry is just as imprisoned as Dr. Manette has been through his work at Tellson´s Bank, but he does become liberated as the novel progresses.