Our project dollar amount has increased by over $2mil
It appears that you may be referring to an update preliminary notice. Once you have given preliminary notice on a project you are not required to update it based on change orders increasing the contract price. If you are entering into a separate contract for the additional work, then you should submit a new preliminary notice. The construction lien (mechanic's lien) is what you would file if you have not been paid and plan to perform no more work until the lien is resolved. If further money became overdue, you would need to file a new lien. Also, if you performed additional work, you would need to record a new lien as additional work invalidates liens recorded before that work was performed.
The question is whether you file an "updated" lien or whether you file/record a new lien. If the initial lien was recorded prematurely, you may opt to record a new lien If not, you may be able to record an "amended/supplemental" lien. With this much money at stake, it makes sense to contact an experienced construction lawyer ASAP!