Doesn't the article contradict what you just said?
"We believe, and Apple’s Security Engineering and Architecture team has confirmed to us, that Lockdown Mode blocks this particular attack," Citizen Lab said.
Apparently it's Apple specific and the android "Lockdown mode" just disables all phone unlock methods (face detection, fingerprint...) other than the main one (pin, pattern...) until the next unlock.
Still good to be aware of in case you're likely to be arrested or something.
The most likely issue you'll encounter is that it blocks almost all message attachment types, so if someone texts you an image, PDF, contact card, etc, it will completely block the attachment.