Unsourced and probably an exaggeration. An alternative calculation is presented by the Handbook of Texas Online by the University of Texas - Austin:
By the end of 1861, 25,000 Texans were in the Confederate army. Two-thirds of these were in the cavalry, the branch of service preferred by Texans. Lt. Col. Arthur Fremantle of the British Coldstream Guards, who visited Texas during the war, observed this fondness for cavalry service: "it was found very difficult to raise infantry in Texas," he said, "as no Texan walks a yard if he can help it"....Approximately 90,000 Texans saw military service in the war. Governor Lubbock reported to the legislature in November 1863 that the army numbered 90,000 Texas residents, but this figure seems high for Texans in service at any one time. The 1860 federal census lists 92,145 white males between the ages of eighteen and forty-five years living in the state. Allowing for a slight increase in population during the four years of the war and considering that some Texans younger than eighteen and older than fifty served, one may say that between 100,000 and 110,000 Texans were potential soldiers.
Two-thirds of the Texans enrolled in the military spent the war in the Southwest, either defending the state from Indian attacks and Union invasion.
If "two-thirds" of "90,000 Texans [who] saw military service" were in the "southwest," that only leaves about 30,000 for Lee and all the other confederates commands outside of the southwest. Maybe rustbucket (ping) has researched this question before.
The number is not as important as the idea.
[cr]: Unsourced and probably an exaggeration.
Lee was appointed general in chief of all Confederate armies in February, 1865. In that sense most of the Texans in the Confederate Army at that time were serving under him, though not in Virginia. However, the Western theater was essentially independent of Lee, given the poor communications and the Union control of the Mississippi.
I don't know how Texans were in the Confederate Army in February 1865. There was also the matter of state troops which would not have been under Lee's command. Based on the names of the various Texas troop units, I suspect that most Texans who served were in the Confederate Army rather than the state troops.