Can two independent sources of light produce interference?

No, two sources of light cannot produce interference. The lightwave emitted by two identical but independent sources, even though they have the same frequency and wavelength they might not have a constant phase difference i.e., they may not be coherent. So, the sustained interference pattern will not be obtained. Due to rapid change in phase difference, the intensity of bright and dark fringes will change rapidly. But as the time persistence of fringes is smaller than the time of persistence of human vision, we will be unable to see the interference pattern formed by the independent source of light. So, two sources of light cannot produce interference.