Hi @Jatin Saini,
Thanks for your trust and we are pleased to offer assistance.
Based on your description, we understand that you are considering using Power Automate to archive your SharePoint lists and want the Lookup columns to be unaffected by the source lists.
The best experience we've had using Power Automate to archive lists is creating a flow to move list items to the archive list at regular intervals. To ensure that no data is lost in the Lookup column, I recommend not using a column of type Lookup in the archive column but using a text to hold multiple Lookup values.
You can get the value of the Lookup column by following the method in this article:
Getting the value from a lookup column in Power Automate
Note: non-official, just for reference.
If you are new to using Power Automate to archive lists, you can refer to these articles:
Archive SharePoint List Items with Power Automate
Note: non-official, just for reference.
Effortlessly Archive SharePoint with Power Automate!
Note: non-official, just for reference.
For the two ways of storing Lookup column data that you mentioned, it is likely that you will need to make a choice based on your actual needs to see which way has more advantages that you need. Divorced from specific needs, we can't tell which of these two approaches is more appropriate.
If you have any questions, please do not hesitate to contact me.
Moreover, if the issue can be fixed successfully, please click "Accept Answer" so that we can better archive the case and the other community members who are suffering the same issue can benefit from it.
Your kind contribution is much appreciated.