Lambert, a senior at SEMO, leaped 6-feet-6 3/4 inches to take second place behind Tennessee State's Buford Williams, who was tied with Lambert, but cleared 6-8 3/4 on his final attempt.
Lambert had one final attempt to clear the mark but barely clipped the bar on his way down.
"If nobody cleared this height I was thinking I had it in the bag," said Lambert. "(Williams) went and cleared it and it pumped me up for one last jump. I thought I got over it pretty good, but it didn't turn out that way."
Williams also captured first in the long jump earlier in the day with a tremendous leap of 25-1 1/4 and he took sixth in the javelin.
After the first day of events, SEMO was in first place with 80 points compared to Eastern Illinois' 66 points.
The final day of the championships was held on Saturday but results were not available at press time.
Lambert also competed in the long jump and was able to garner points with a seventh place finish with a leap of 23-2 1/2.
"I haven't been jumping that well in the long jump the last few meets and I haven't been focusing all my attention on it," said Lambert. "I came out and jumped as far as I had all outdoor season. The competition was tough."
Lambert captured first in the high jump in last year's championship meet. While he admitted he was disappointed not to repeat, he's more worried about getting the team championship.
"Second place is nothing to hang my head about," said Lambert. "We all jumped pretty well today. I can't be disappointed about anything. We went 2, 5 and 7 to put us ahead of EIU. I'm disappointed a little bit, but I worked hard this whole season. We're in the lead after these first few events so I'm not that disappointed."
Lambert was also recently named the OVC Indoor and Outdoor Field Athlete of the Year. He also received the honor two years ago when he was a sophomore at SEMO.
His teammate, Miles Smith, was named the OVC Indoor and Outdoor Track Athlete of the Year.
Smith is undefeated in the 400 meter dash and he won Friday's prelim race easily with a time of 47.13.
"It's an honor," said Lambert. "I won it a couple years back as a sophomore because I was doing three events every meet and bringing in a bunch of points. I just stay steady and do my average jumps every meet. Sometimes I come out and have an extra good week. I'm not sure what to say about it, but it's a good honor."