To appreciate and understand the figurative meaning of the expression clearly, one needs to know the context in which the line was spoken, and by whom it was uttered.
Firstly, these words are spoken by Macduff in Act 2, scene 4, when he comes upon Ross and an old man who are discussing the unnatural events they have witnessed, as well as King Duncan's murder. Macduff seems very upset about the murder and his tone is quite abrupt and clinical. He reports events as they had been conveyed to him or as he had seen them.
His remark stems from Ross's enquiry of whether he would attend Macbeth's investiture as king at Scone, since Duncan's two sons had fled the country, creating suspicion that they had bribed the guards who Macbeth had killed for their father's murder. It is clear from his tone and expression that Macduff does not entirely believe this version.
Macduff tells Ross that he would not be in attendance at Macbeth's coronation and would be going to his own castle. When Ross informs him that he was going, Macduff utters these words:
Well, may you see things well done there: adieu!
Lest our old robes sit easier than our new!
What he says is rich in irony. Firstly, he expresses the hope that Ross may see things go smoothly at Scone, unlike the manner in which things had recently transpired.
Secondly, he uses metonymy (part representing a whole or vice-versa) when he refers to 'robes'. He is obviously referring to the cloak worn by the king on his coronation and other official functions and also, to the attire they would wear in their current (new) positions.
The implied (figurative) meanings in these instances is that he expresses doubt that Macbeth could measure up to the stature of King Duncan. They may find themselves uncomfortable with his new rule. Secondly, since the king is now dead, they have to become accustomed to their new positions in relation to their soon-to-be ordained monarch, Macbeth.
This, of course, does not sit well with Macduff since he is highly suspicious of Macbeth. He therefore refuses to show him any allegiance and decides not to attend the coronation.