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Bin workers who belong to the Unite union began an all-out strike on 11 March, following sporadic walkouts since January.
"Right now it does feel like there's sort of layers on layers of bad news coming out of the Midlands, but I'm very hopeful that we will find a way through," Lycett said.
The comedian has often used his career to boost his hometown, presenting a live late-night show from Birmingham in 2023 and 2024.
The show, Late Night Lycett, won a Bafta in 2024 and involved a training scheme that offered work to local people.
Lycett has a new show due to air this month, for which he has visited places called Birmingham in the US and found links with his hometown.