No. There is no missing conjunction.
There's a play on "look to", which means both "try to" and the literal "take a look at". There is also a typical poetic inversion of verb and object. Note also that in Shakespeare's day "if" used to take the subjunctive, so (uninverted) we have "if looking move liking" instead of the modern "if looking moves liking". The similarity of sound between "look" and "like" makes the passage an even greater delight!
"I'll look to like" = I will try to like you. (I think an alternate interpretation might be "I'll show I like you.")
"if looking" = if taking a look (at you)
"liking move" ("moves liking") = moves me to like (you).
(but I won't look any more deeply than you consent to)
I don't think I'm very far off, but consulting a scholar of Shakespeare wouldn't hurt.!
![Smile [:)]](/emoticons/emotion-1.gif)
After reading Mr. Micawber's response I got out my copy of the play, and I see that it is more like:
I will try to like him (Paris), if looking moves me to like him [not "you"!]. The "you" in the second part remains "you" because it refers to Lady Capulet, whom she is talking to.