Lee, who is a friend of Reid's son, said: "For some reason the senator, then a congressman, decided to lock me in the garage. I think he kept me in there for a good half hour," said Lee on MSNBC's "Morning Joe" Tuesday. "I was about 12 or 13. I'm sure I deserved it."
Lee said that Reid and his family were the first "real" Democrats he knew and praised the majority leader's sense of humor.
"I discovered in their home I couldn't tout the virtues of Ronald Reagan without expecting a fight … they were good times," Lee said.
Despite his personal relationships, Lee blamed Senate Democrats for preventing passage of a budget.
He told MSNBC he believes the other side of the aisle has not passed a budget because they don't want to expose themselves to controversial votes as they prepare for reelection.
"I think in time they'll see that they've done this at their own peril," Lee predicted.
When asked which budget proposals have a chance of being signed into law, Lee said, "I don't know."
"At a time we've gone 900 days without a budget, when we've had Republican proposals put forward and voted down by the Democrats … I'm not sure, without a change of heart on the part of the Senate Democrats, what can get done."
However, Lee said he has "constantly" met with Democratic colleagues to try to agree on a balanced-budget amendment, noting this is an issue he feels very strongly about.
The Utah senator also said he would not support a balanced-budget amendment that allows Congress to vote for an exemption during times of military conflict.
"That's always present, that's not really a balanced-budget amendment," Lee said.
One area where he didn't disagree with Democrats was over the Obama administration's military drawdown from foreign conflicts.
"Let me put it this way,” said Lee. “The president is working on plans to start withdrawing from some of these battlefields in which we're engaged and I don't disagree with that."