Lissemore, who enters his fourth season, also played at William and Mary.
"When I first got (to William and Mary), I was actually scared of him," Webb said. "He didn't talk, this big guy, he was quiet. As the year went on, we got along real great. He came and saw me when I was at the facility, we definitely kept in contact."
During his predraft visit, Webb got a tour of Cowboys Stadium, the practice facility at Valley Ranch and stayed at the team hotel, the Gaylord Texan.
The massive facility, that houses the team prior to home games, impressed Webb.
"I don't think I really seen a hotel (that big)," Webb said. "I got to meet all the coaches, Jerry Jones and everybody, Jason Garrett. I loved every part of it."