The 29-year-old stopper joined as a free agent as cover when Adam Bogdan suffered a knee injury, originally penning a short-term deal.
The former Millwall keeper will now be staying on into the new year after penning another month at the club.
The move is timely with current number one Andy Lonergan a doubt for the Boxing Day trip to Barnsley after injuring his elbow in Saturday's home draw with Charlton.
If Lee-Barratt is needed to step in, with Bogdan still sidelined, it will be his first senior action since April 2012 when he turned out for Ipswich against Doncaster Rovers.