Lee, who was the chief equity strategist at J.P. Morgan before co-founding Fundstrat, said his firm has an indicator to measure alt-coins, which is "the percent that have tripled over 90 days."
On Jan. 13, the indicator hit 78 percent, "which is normally a top," he said.
"In January, we thought you need to rotate back into the large caps because that's what happens," he said. "And this indicator has been falling, but yesterday it fell to 3 percent."
He said he expects the lesser-known, smaller coins will remain in "purgatory" and not begin rallying until at least the middle of August, if not mid-September, due to regulatory uncertainty.
The U.S. Securities and Exchange Commission has taken a tougher stance on cryptocurrencies in recent weeks, issuing dozens of subpoenas and calling for some digital asset exchanges to register with the agency.
In a late February report, Lee said investors should avoid alt-coins until late March or early April based on historical performance of previous sell-offs and subsequent rallies. The value of all cryptocurrencies excluding bitcoin has roughly halved from $376 billion in late December to $193 billion Tuesday, according to CoinMarketCap.
Lee still expects bitcoin to reach $20,000 by the middle of the year and $25,000 by the end of the year, he said.
The bitcoin bull, who is the only major Wall Street strategist to issue formal price targets on bitcoin, pointed out that the amount of time that bitcoin fell below $6,000 this year was relatively short.
"If you count the number of hours we've spent below $6,000 recently, it was less than an hour," he said, adding that, in February, investors only had an hour to buy bitcoin below that price.
The "fully-loaded cost of bitcoin" around the world, Lee said, is around $8,000.
"So you're buying bitcoin around cost today," he said. Bitcoin prices hovered just under $9,000 on Tuesday evening.
— CNBC's Evelyn Cheng contributed to this report.