That doesn't sound right. Lynx is an Ademco product. Honeywell bought Ademco. The other Ademco products are also part of the Honeywell line. What Ademco system are they claiming is being replaced by the Lynx?
Fire signals typically make up less than 0.5% of all alarms. There's no justification for charging an extra $3 per month for monitoring fire.
Unless they disable the on-board sounder and install a separate keypad and siren, nix it. The system can be defeated in a few seconds before it ever gets a chance to report.
They're the functional equivalent of an ADT "authorized dealer" except that the monitoring is being done by Monitronix. I know of at least one Moni dealer who operated for years without a license with Monitronix' full knowledge and consent. During that time the dealer ripped off hundreds of families in Connecticut. He actually signed on with Protection 1 at first, just to get Honeywell's distributor to sell to him (they at first refused as he had no credentials and no experience). Once he got in he quickly switched to Moni where he was allowed to continue defrauding people in CT until he skipped out.
Based on that dealers actions, of which Monitronix was fully aware, I could not recommend them.
Be very careful.