Is there an established way to lobby arXiv to expand the paper subjects it covers?
Only arXiv offers the guarantees against new takeovers.
All the cloud services around might suddenly change their open policies at best. 

arXiv   platform is well engineered and there is already a Quantitative Finance category, adding more in the economics side should not be a problem, if they are willing to. 

One possibility is to start a campaign on specialised webservices such as change.org. 

With a lot of people asking, they might easily take into consideration the proposals to widen their scope. 

The major problem would be how to advertise this  campaign. Your question got an average 80 views in 10 days.