The decision was taken in mutual agreement with the players in wake of COVID-19 pandemic.
Watling was due to play the first nine rounds of the County Championship while Maxwell and Faulkner were set to take part in the club's T20 Blast campaign.
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“I would like to thank BJ, Glenn, James and their representatives for their total understanding of the current situation and full agreement of this decision," said Lancashire’s Director of Cricket, Paul Allott, in a media release.
"We were all looking forward to welcoming BJ Watling to Emirates Old Trafford for the majority of our Specsavers County Championship campaign, whilst welcoming Glenn and James back to the Club for our Vitality Blast campaign."
"These are clearly very uncertain and challenging times for all counties both financially and operationally and it’s clear the issues we face at the moment will have an impact on the way we prepare for the domestic season," Allott added. "The overseas player situation is a policy that has been discussed nationwide and we think it’s prudent to mutually come to an agreement with the players we had originally signed."
"We will keep in touch with the players and their representatives, and as part of the agreement we’ve come to, we do have an option to sign them for the 2021 campaign."
Lancashire has also announced a 20 per cent salary reduction for all its staff in the month of May so as to help the club overcome these difficult times.
"This has also been unanimously agreed to by the Lancashire players. The pay cut has been agreed by the playing squad following a number of conversations between Lancashire Cricket and several of its senior players," reads the club's statement.