President Donald Trump’s personal lawyer helped a major donor to Mr. Trump’s inauguration pitch a nuclear-power investment to the Qatari sovereign-wealth fund at a meeting in April, according to people familiar with the matter.

The donor, Franklin L. Haney, is seeking to complete a pair of unfinished nuclear reactors in Alabama known as the Bellefonte Nuclear Plant. His company is lobbying the Trump administration for an extension of tax credits, federal disclosures show.

Mr....