They have ignored repeated attempts to collect. This is an HOA that won't pay their bill. Do we have a right to lien for non-payment of material & labor that was done on the common areas? If so, how does it work with the residents of the HOA in addition to their Board?
Yes, if you are a contractor and you provided services or materials to repair or improve the property at their request and you otherwise complied with the contract (and you are still within yor 90-day window).
Yes, if you provided labor and/or materials at the request of the HOA for the common areas, you certainly have the right to claim a lien and to record your lien claim.
The threat of the lien may be very powerful, so if you have the time, it would make sense to make a final demand and let them know you are going to file a lien against the common area property if you are unpaid.
A claim of lien can be foreclosed, which is really the entire point. That's why a lien is such a powerful tool to get paid. You can pursue the common area as you could any other property that is subject to a lien. It's difficult to understand if the HOA doesn't care because the land has value as it relates to the subdivision. But in any event you will need to prove your claim, which involves proving the value of the work you provided at their request.
I think they will care about the lien because it is something for which they are accountable to their owners. They may be required to bond it off which would work to your favor.