Although Lady Macbeth does not seem to have any overt relationships with other characters, she is deeply affected by the murders as evidenced by her breakdown. Apparently, Lady Macbeth must have felt some affection for Banquo, King Duncan and Lady Macduff and her children, she goes mad with guilt thinking about them. Lady Macbeth says in Act V, Scene I
"The Thane of Fife had a wife:
where is she now? What! will these hands ne'er
be clean? No more o' that, my lord, no more
o' that: you mar all with this starting".
This obviously reflects her guilt, but if she didn't care at all, why would she be so remorseful, so troubled? The murder of Lady Macduff and her children deeply troubles Lady Macbeth. At the end of the play, it seems that Lady Macbeth cares more for the murder victims that she does her husband, with whom she had such a close relationship in the beginning
Lady Macbeth has very limited interaction with other characters in the play. In Act 1, sc.6, when Duncan arrives, she greets him as a hostess receiving such an honor should. In Act 2, sc. 1, Banquo makes reference to a "diamond" with which Duncan has given to Lady Macbeth. It's not clear whether this is an actual gem or if it's a metaphor for the honor of being a visitor in Lady Macbeth's house. Regardless, it's still not much interaction, especially since it appears that the gift is presented through Banquo to Macbeth before getting to Lady Macbeth. In Act 2, sc. 3, when Duncan's body is discovered, nothing more than the usual and expected responses are made to Lady Macbeth. At the banquet in Act 3, sc. 4, Lady Macbeth calls the guests "worthy friends" and "good peers", but it lacks sincerity. She has no more interaction until Act 5 when she has gone mad and it appears then that most of her interaction is with her lady in waiting. Finally, at the end of the play, in Malcolm's final speech, he refers to Lady Macbeth as Macbeth's "fiendlike queen". The relationship Lady Macbeth had with other characters was limited or not good. Apparently other characters saw her as the conniving, ambitious woman that she was.