William Ackman’s Pershing Square Capital Management LP is joining another activist investor in Lowe’s Cos., hoping to profit as the retailer tries to make improvements under a new chief executive.

Pershing Square has built a stake in the home-improvement chain valued at roughly $1 billion as of Tuesday’s close in what is expected to be a friendly investment, according to people familiar with the matter. Lowe’s had a market value of roughly $78.3 billion at Wednesday’s close.

Mr....