There are grave fears for the two men after their old Chevy van was found destroyed by fire on a dirt road in a rural area of Sinaloa state.
Two bodies were found inside, with the results of DNA and other forensic testing expected to confirm whether they belong to Mr Lucas and Mr Coleman.
"There is a commitment by the investigating authority to resolve the case immediately and arrest those who caused this serious damage to these two people," Sinaloa's tourism secretary, Francisco Cordova Celaya, told Mexico's Noroeste news website.
Mr Celaya said he feared the incident would have a negative impact on tourism in Sinaloa and the state's international image.
A team of special agents will be formed to investigate.
Mr Lucas and Mr Coleman went missing on November 20 while driving across Sinaloa.
The van, with Canadian number plates, was found on a dirt road near an irrigation channel with the badly charred bodies inside.
The men, both 33, had been living and working in Edmonton, Canada, and drove the van down to Mexico for a surfing safari and to catch up with Mr Coleman's Mexican girlfriend, Andrea Gomez.
After surfing in Baja, the men caught a ferry with their van to the coastal port town of Topolobampo.
They planned to then drive 800km to Ms Gomez's home in Guadalajara.
Mexican authorities are checking the identities of other passengers on the ferry and highway toll booth cameras as it appears the men went missing early into their drive.
When the men failed to contact Mr Lucas' English girlfriend in Canada, Josie Cox, or Ms Gomez, authorities were alerted.
The families of the two men have been overwhelmed by public support, with a gofundme.com page set up to raise money to pay for family travel costs to Mexico, and if their worst fears are realised, take the bodies back to Australia.
It has raised more than $50,000 in just two days.
Sinaloa is the home of the notorious Sinaloa Cartel, headed by fugitive kingpin Joaquin "El Chapo" Guzman.
The US State Department warns citizens against travel in remote areas.
