Paulson has made more than $1 billion investing in Lehman claims already, as previously reported by The Wall Street Journal. The exact size of its remaining position was unclear. Representatives for Paulson and King Street declined to comment.
The debtholders aren't public, but hedge fund firm Halcyon Asset Management has also been reported to have made money off Lehman claims in the past. A spokesman for Halcyon declined to comment.
Read MoreLehman payout tops $80 bln, creditors get another $17.9 bln
The original bankruptcy plan estimated that bondholders would get about 21 cents for every dollar of assets; the total is now 26.9 cents. With previous distributions, the total market value is about 43 cents, according to a person with knowledge of the payments.
Read MoreFreddie Mac gets (some) money back from Lehman
Lehman, the once-prominent investment bank, filed for bankruptcy in September 2008 at the height of the financial crisis. So-called vulture investors soon snapped up claims on the company's debt, often buying from other parties who preferred a quick payout instead of waiting years to try and get more of their money back.
Lehman's estate has benefited recently from settlements with the Internal Revenue Service, Fannie Mae and Freddie Mac. That gave the company more money to pay off its creditors.
Read MoreLehman Europe creditors set for extra $8 billion
Other hedge funds like Elliott Management and Baupost Group have separately invested in Lehman's European business, Lehman Brothers International Europe. Elliott and Baupost declined to comment.