For a quick anwer : 

1. Is there a way to set a default value to a lookup field in Nintex Forms?

=> No, there is not way to set a default value for lookup fields from a forms

2. Also, Is there a way a value (ex.. from another field) can be set to a lookup field using rules?

=> No, there is no way to set a value  from a forms

The concept of a lookup is that the data is store in an other list, this data can be update/delete. If you force a default value, oneday, if this value is delete from the source list, you will have a problem. That way you can't for ce a default value from the forms.

But you can made it from a workflow.

For exemple : in your workflow, if your field is empty, make a query to your source list, get your item ID, and set this ID in your field of your current item.

Thank you so much for the elaborate clarification and the possible workaround using a workflow. Appreciate much!!

I understand the concept of the lookup fields and in my opinion also it should work like that. The scenario where it hinders the user experience is when working with conditional dropdowns. 

As far as I know lookup field is the only way with which we can implement a conditional dropdown field in Nintex. To ease the end user experience, I wanted to have some of the conditional dropdown values pre(auto)filled based on certain conditions. (Microsoft predecessor InfoPath does that).

Had Nintex provided an alternate solution for conditional dropdowns prefilling, it would have done my purpose. I wish to see this in Nintex.

I have been able to set the value of a lookup and default the value of a lookup. I require the use of additional fields. My initial lookup is usually set to hidden. or some way I can toggle to confirm data is written back. I create a text field, and connect it to the lookup field. All you have to do is use a rule to set the text field and it will default the lookup. when setting the text field you will need the entire value, ID;#Value.

Have you done this in Classic or Responsive forms? Please share solution in more details.