While not 100% clear, this was probably Morgoth
While it may initially seem obvious that this was Sauron, given he was the Lord of the Ringwraiths and it was the Witch King who initially trapped the wights in the Barrow Downs, it is not so easy to make that claim.
The Witch-king had now a clearer understanding of the matter. He had known something of the country long ago, in his wars with the Dúnedain, and especially of the Tyrn Gothad of Cardolan, now the Barrow-downs, whose evil wights had been sent there by himself.
Unfinished Tales - The Hunt for the Ring
The references in the poem seem to link most likely to Morgoth, the first Dark Lord, especially given the failing of the sun and the death of the Moon. This line seems to ring very closely true with the prophecy of his return and the Dagor Dagorath.
For 'tis said ere the Great end come Melko shall in some wise contrive a quarrel between Moon and Sun, and Ilsinor1 shall seek to follow Urwendi through the Gates, and when they are gone the Gates of both East and West will be destroyed, and Urwendi and Ilsinor shall be lost.
History of Middle-earth: The Book of Lost Tales - Part One, Hiding of Valinor
1 Note that Urwendi and Ilsinor are the guides of the Sun and the Moon, renamed Tilion and Arien in the Silmarillion.
When the world is old and the Powers grow weary, then Morgoth, seeing that the guard sleepeth, shall come back through the Door of Night out of the Timeless Void; and he shall destroy the Sun and Moon.
History of Middle-earth V: Quenta Silmarillion, Chapter XI - Later Quenta Silmarillion, Last Chapters
More on the Dagor Dagorath can be read here
This seems to parallel Tom later banishing the wights to a place which sounds similar to the Doors of Night and the Void
Lost and forgotten be, darker than the darkness,
Where gates stand for ever shut, till the world is mended.
The final bit, "Where gates stand for ever shut, till the world is mended*", again seems to suggest similarities to the Doors of the Night and Dagor Dagorath, when Arda Marred is broken and a pure Arda is reborn. (As can be read above)
There is however a reference, which is often used for Sauron throughout the books and in this poem as well.
till the dark lord lifts his hand over dead sea and withered land
This reference to a had stretch or being lifted over the land occurs quite often throughout the novel:
'[Sauron’s] arm has grown long indeed,’ said Gimli, `if he can draw snow down from the North to trouble us here three hundred leagues away.’
‘His arm has grown long,’ said Gandalf.
This however is the only reference to Sauron in the poem, outside that listed at the top.
The destructive hand could also be interpreted as Morgoth's destruction of the work of his fellow Vala:
In the black wind the stars shall die ... lifts his hand over dead sea and withered land
The stars, originally created by Varda, the sea was Ulmo's work and the land Yavanna's. The destruction of the three is the destruction of the work of his brothers and sisters, if the hand were to destroy them, it would carry out Morgoth's original purpose.