This answer to What kind of triangle is formed by three unequal masses in a circular restricted three body orbit? explains that
In the Newtonian limit, an equilateral 3-body solution exists for any combination of masses
and links to Triangular solution to general relativistic three-body problem for general masses which stars with "Lagrange’s equilateral triangular solution for the three-body problem" and looks at relativistic ("post-Newtonian") effects.
In the circular restricted three body problem of Lagrangian points fame one body is a "test mass" with no significant effect on the other two, but apparently three massive bodies can also have a circular orbit solution where they still form an equilateral triangle, as $L_4$ and $L_5$ do in the CR3BP.
Where did Lagrange first write about the equilateral triangular solution for the three-body problem where all three bodies have non-zero mass?