Getting Invisalign After Dental Crown?

Unless there is active infection (decay) present, I recommend my patients have Invisalign treatment BEFORE their restorative dental treatment. I like to get the teeth aligned ideally first. This enables me to be more conservative with the dentistry afterwards.

As a rule we (orthodontist) recommend waiting for major final restorations (Crowns, veneers) until after your orthodontic treatment is finished.
The main reason is the you want to build new crown to the new teeth position and bite and not vice versa.
Now, the dentist might have compelling reasons for them to do the crowns before such as, fear of the tooth not lasting that long because of large cavity underming the tooth structure etc.
So please check with an orthodontist and dentist what would be best for you.

Ideally, Invisalign first.
As soon as the crown is seated, Invisalign treatment can start (there are no barriers). When gaps are present, it is common that the gaps get closed when making the crowns. However, if only 2 teeth are restored, it can result in teeth with unnatural proportions (look too fat). If the plan is backwards, doing invisalign after the crowns, the lab could be told to leave the gap so that it can be closed with Invisalign.