Why should Lincoln consider give that any thought. Several Generals in the Federal Army owned or had owned slaves during there term of service, it was not against the law. Whipping a slave was legal in the eyes of Virginia law. It was an acceptable form of corporal punishment. Lee was in a position to have such punishment carried out. Why would having a couple of recalcitrant runaway slaves whipped be out of the realm for Lee to do. He had many men in the Army of Northern Virginia shot for the exactly same offence, running away.
You make a point. Not only was whipping legal under Virginia law, it was legal under federal law. The United States Navy flogged many until the practice was outlawed by Congress in 1850. These were U.S. service members being flogged under the aegis of the United States government.
To my knowledge, prior to Congressional action, the U.S. Supreme Court never ruled the practice prohibited under the eighth amendment.
I'm not sure what punishment was available to runaway slaves who may have worked building the U.S. Capitol.
Some sates continued the practice of whipping well beyond slavery days. Take Delaware for example. They whipped prisoners up until about 1952 and formally abandoned the practice in the 1970s.
The reason I question the claims concerning Lee is that the accounts conflict.