What does "one needn't stand on trifles" mean?

Solution 1:

To stand on something means to insist on something, to be particular about something in this sentence.

Trifles are trivial things, things that are of little importance.

Hence your sentence means after that, it is unnecessary to be particular about trivial things. I don't know the story, which is why I don't know exactly why her aunt says this. Perhaps she means that refusing a lord increases a woman's status so much that, afterwards, one may safely risk some loss of status due to less reputable behaviour. Or perhaps it is just that, after this important event, anything else probably fades in comparison.

Solution 2:

"Refusing an English lord" is a MOMENTOUS (social) undertaking. After doing that, anything else the lady could do would seem trivial "trifling," by comparison. Which means she can do anything at all, with less of an impact on her life than refusing the lord.