A tweet sent by the BBC at 1.14am on December 31 read: "We're aware of a technical issue affecting the BBC website and are working to fix this now. We'll update you as soon as we can."
Mr Lynam told BBC Breakfast that the corporation's technology correspondent Rory Cellan-Jones had received a tweet from a group calling itself New World Hacking (NWH), claiming responsibility for a distributed denial of service (DDoS) which bombarded the system with messages.
Mr Cellan-Jones tweeted a message he received from NWH on the DDoS which said: "It was only a test, we didn't exactly plan to take it down for multiple hours."
The group claimed responsibility and said its real aim is to stop potential online propaganda from IS.
Mr Lynam described the group apparently claiming responsibility as "quite a serious claim to make" although the BBC "cannot verify or prove their claims". NWH claimed it was testing the power of its own servers.
Mr Lynam said: "Their ultimate goal, believe it or not, is not to attack the BBC but to go for Isis, the group which often calls itself Islamic State, and all their servers so they cannot spread propaganda from various different websites.
"What this group does is to take down various different websites it believes to be criminal and leading to terrorist acts. It posts the website which has been taken down with the hashtag 'tangodown' or 'takenddown' deliberately by a distributed denial of service (DDoS), which is what hit the BBC two days ago.
"We have to stress we have no evidence but this group is claiming responsibility for this DDoS attack and they claim their ultimate goal is to take down Isis websites."