There are quite a few passages in Lucretius' De Rerum Natura (more than just these) which describe dependent origination, but here is one section, Bailey translation:
1-803
‘But,’ you say, ‘the facts show clearly that all things are nourished and grow from the earth up into the breezes of the sky; and unless the season at a propitious time fosters them with rain, so that the trees rock beneath the outpouring of the storm-clouds, and the sun for its part cherishes them, and bestows its heat on them, crops, trees, living creatures, none could grow.’ Yes, in very truth, unless we too were nurtured by dry food and soft moisture, we should lose our flesh, and all the life too would be loosened from all our sinews and bones. For beyond all doubt we are nurtured and nourished upon things determined, and other things again, each in their turn, on things determined. Yea, we may be sure, it is because many first-beginnings common in many ways to many things are mingled among things, that so diverse things are nourished on diverse food. And often it is of great matter with what others those first-beginnings are bound up, and in what position, and what movements they mutually give and receive; for the same build up sky, sea, earth, rivers, sun, the same too crops, trees, living creatures, but only when mingled with different things and moving in different ways.
1-823
Indeed scattered abroad in my verses you see many letters common to many words, and yet you must needs grant that verses and words are unlike both in sense and in the ring of their sound. So great is the power of letters by a mere change of order. But the first-beginnings of things can bring more means to bear, by which all diverse things may be created.