Cinco de Mayo commemorates the Battle of Puebla on May 5, 1862. Lew was busy with the aftermath of the Battle of Shiloh in the area of Corinth, Mississippi, at the time, and may not have heard about the battle until long afterwards. Puebla certainly had little impact on his life for two years.
Then in 1864, Lew was sent to Mexico under Grant's orders. During an interview with Frank G. Carpenter, Lew related the circumstances of that mission:
I was the agent of General Grant in giving the Mexicans such assistance as enabled them to keep their country a republic; Louis Napoleon wanted to make it a monarchy. He was backing Maximilian, and was in a fair way to succeed. This was just at the close of the rebellion, when we were still in an unsettled condition, and did not dare risk a war with France.
I was sent by General Grant, without the knowledge of Secretary Seward, to consult with General Juarez, the Mexican President, to see if we could not in some way assist the republic. I went to the Rio Grande and pushed my way through the country to Chihuahua, where I met Juarez. He was in a bad way; had but few troops and but few arms, and it looked as though Maximilian must succeed. We discussed the matter, and as a result he sent the Governor of Tamaulipas with me back to the United States; and there in connection with Matias Romero, the Mexican Minister to Washington, we bought about $5,000,000 worth of Winchester rifles, cannon, and other munitions of war, and paid for them with Mexican Government bonds.
We put these arms on a ship and, in broad daylight, started for New Orleans as our nominal port. After a while we changed our course and made for the mouth of the Rio Grande, where we unloaded the guns and passed them on to the Mexican troops. These guns changed the tide of victory. From that time on President Juarez conquered, until finally he executed Maximilian at Queretaro.
It's safe to say Lew had a strong interest in the Mexican Republic. According to Wikipedia, Cinco de Mayo was first celebrated by Californians during the Civil War, as well as in Mexican-American communities in the western parts of the United States. So Lew probably didn't spend May 5 drinking margaritas and singing Mexican folk songs, but he definitely contributed to the overall cause behind Cinco de Mayo.