The former Manchester City and Everton centre back has struggled to overcome injuries and is unlikely to make a comeback this season due to lack of fitness
The 33-year-old Republic of Ireland international has been out of action since the summer of 2012 as a result of recurring shoulder and groin injuries. The defender has undergone surgery in order to correct the issue with his groin but has struggled to regain full fitness.
"He is still not ready to start playing again," Lambert said. "Richard's injury is one of the most frustrating I've seen. It's been stop and start for him.
"It's been most frustrating for Richard to get back. We just have to see how he progresses over the rest of the weeks this season."
Dunne, who is out of contract at Villa Park in the summer, has been linked to a number of MLS clubs, including New York Red Bulls and LA Galaxy.
Meanwhile, West Brom striker Shane Long may be on his way out of the Hawthorns, after attracting interest from Italian and Spanish clubs, according to a report in The Mirror.
The former Reading frontman, who is currently in the middle of contract negotiations with the Baggies, is said to be a target for Serie A club Lazio and La Liga side Sevilla.