The terminal shown in the schedules as "Lexington Avenue" was a temporary station opened in the basement of the Grand Central Palace on Lexington Avenue between 43rd and 44th Streets. As Ridgefielder surmised, it was opened about 1907 to provide additional platform space for trains during the demolition of Grand Central Station and the construction of Grand Central Terminal.
It's very hard to find information about the temporary terminal though there is a reference in paragraph 17 of this pretty good capsule history of Grand Central
Looking at old newspaper articles, commuting into Grand Central was very difficult during the construction of the new terminal. Commuters wrote many exasperated letters to New York City newspapers. One I especially remember reading was from a Harlem commuter who complained of not knowing if the temporary walkway he used in the morning to get out
of the station would still be there that evening when he was trying to get in
Grand Central Palace was an exhibition hall and was itself demolished about 1913 I guess. The Graybar Building was later built on the site (by New York Central) while a new Grand Central Palace opened on Lexington between 46th and 47th Streets about 1911.
The New Haven tried to assist during this difficult time by adding service on the Harlem Branch to the old 132nd Street terminal in the Bronx, hoping to reduce the flow into Grand Central. I don't believe that was very successful though -- it was just too far uptown for most people to want to bother with -- and many of the extra trains were soon discontinued.