Question

A party to a lawsuit that has an actual stake in the outcome of the case has:

Answer 1

This is called standing or locus standing. This is where a party can sufficiently demonstrate a connection to a case. That any result would affect him. The gravity of the outcome would depend on the amount of involvement the party is to the case. 

Answer 2

I believe the answer is Legal standing.
People who had a legal standing are the one that will recieve either harm or benefit after a decision is made.
The amount of involvement that certain parties had in the case will determine how much involvement the party is allowed to influence the case.