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...

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:

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"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.