The left-hander asked for a raise from $2.75 million to $5.7 million during a hearing Wednesday before a three-person panel. The Nationals argued he should be paid $5 million.
A decision by arbitrators Robert Herzog, Elizabeth Neumeier and John Skonier is expected Thursday.
Lannan was 10-13 with a 3.70 ERA in 33 starts last season.
Twenty-four players remain in arbitration, with hearings scheduled through Feb. 17.
Players won two of three hearings last year. Teams have a 286-212 edge since the process started in 1974.