Speaking in his first appearance as new co-host of AFL.com.au's Access All Areas on Monday, Lyon said Franklin had made a "pretty ordinary" start to his Swans career against the Giants.
On a wet night not suited to tall forwards, Franklin kicked 1.1 from just seven possessions and took four marks as the Swans suffered a shock 32-point loss.
"The one thing I would say is maybe there was an over-correction from his teammates. I would have liked to see a bit more support for Buddy throughout the course of this game," Lyon said.
"I reckon they tried to ram home the whole Bloods culture, 'Let's not make a big deal out of one player', but sometimes you've got to go and support your mate.
"And, look, he was copping it from Toby Greene, he was copping it from everyone out there."
Co-host Damian Barrett said he feared Franklin's $10.2 million nine-year deal with the Swans would become a major problem for the club.
But Lyon reserved his judgement.
"I'm prepared to hold my fire because this is one of the great forwards of the modern era and I'm going to back him to get in and have an impact on this game."
You can watch Access All Areas on AFL.com.au every Monday morning.
Twitter: @AFL_Nick
