Conservation of matter: yes.
Atoms cannot perish, and they have probably always been; Epicurus and hence Lucretius argue that the universe must always have existed, since otherwise it would have emerged out of nothing, which is to them impossible. Whenever an object is destroyed, its atoms must go somewhere; and, whenever an object is created, its atoms must come from somewhere.
Similar views had been quite popular among Greek natural philosophers. Heraclitus (c. 535 – c. 475 BC) before them said it like this:
πάντα χωρεῖ καὶ οὐδὲν μένει” καὶ "δὶς ἐς τὸν αὐτὸν ποταμὸν οὐκ ἂν ἐμβαίης"
"Everything changes and nothing remains still... and... you cannot step twice into the same stream" — (Wikipedia)
By this he meant that a stream is never the same because it consists of different bits of water each moment. Democritus (ca. 460 BC – ca. 370 BC) probably inspired Epicurus a great deal with his atomism, which includes indestructible atoms that cannot be created or destroyed but have always been. Both Democritus and Epicurus/Lucretius held that there were different kinds of atoms with different shapes, which affected the properties of the objects composed of these atoms.
Conservation of energy: probably not.
Lucretius did not really have a concept of energy as in modern physics. Heat consisted of some kind of fire atoms, so that would probably fall under conservation of energy; but others kinds of energy, like potential energy, probably did not—or, rather, it would be better to say that he never expressed an opinion about it.
The soul, which is destroyed upon the death of the body, consists of air atoms and guides the body with air. This too was a popular concept in Antiquity: ghosts, phantoms, life force, etc. are often said to be related to air and wind. Latin spiritus ("spirit, breath") comes from spiro, "to blow", as in divine breath. Animal "animal", anima "life force", and animus "mind, emotions" all come from a stem that means "breath, wind" (cf. Greek ἄνεμος /anemos/, "wind"). So perhaps the combination of air and fire atoms could be considered a semi-equivalent of energy; but there are still many other forms of energy that he simply did not consider as such, nor could air be converted into fire.
If one reads the whole De Rerum Natura, the impression one gets is that Lucretius simply did not concern himself with the question of energy in the modern sense. He just assumed that atoms could move for various reasons, without mentioning energy as a separate factor.
However, I have no doubt that he would have eagerly accepted the modern concept of conservation of energy once explained to him, because it would fit his other theories remarkably well.
I don't know Heraclitus very well; we do not have a great deal left of his writings; and his style is rather enigmatic: however, he believed that the entire universe was somehow based on fire. It was the basic element of everything; it caused all the other elements to be. If you compare this to the the modern law of the conservation of energy and the equivalence of mass and energy, perhaps he was not too far off. But it is very hard to interpret how Heraclitus intended this primacy of fire; perhaps it is quite different.