It's actually both. Bear with me; I'll explain.
In the first half of Ezekiel 28:1-19, Ezekiel seems to be referring to a human man.
Ezekiel 28:1-10 (ESV)
1The word of the LORD came to me: 2 "Son of man, say to the prince of Tyre, Thus says the Lord GOD:
"Because your heart is proud,
and you have said, 'I am a god,
I sit in the seat of the gods,
in the heart of the seas,'
yet you are but a man, and no god,
though you make your heart like the heart of a god—
3 you are indeed wiser than Daniel;
no secret is hidden from you;
4by your wisdom and your understanding
you have made wealth for yourself,
and have gathered gold and silver
into your treasuries;
5by your great wisdom in your trade
you have increased your wealth,
and your heart has become proud in your wealth—
6therefore thus says the Lord GOD: Because you make your heart
like the heart of a god,
7therefore, behold, I will bring foreigners upon you,
the most ruthless of the nations;
and they shall draw their swords against the beauty of your wisdom
and defile your splendor.
8 They shall thrust you down into the pit,
and you shall die the death of the slain
in the heart of the seas.
9 Will you still say, 'I am a god,'
in the presence of those who kill you,
though you are but a man, and no god,
in the hands of those who slay you?
10 You shall die the death of the uncircumcised
by the hand of foreigners;
for I have spoken, declares the Lord GOD."
I doubt that Satan (Lucifer) would be called a man or would he be able to die at the hands of humans.
But...the second half seems to refer to a spiritual being.
Ezekiel 28:11-19 (ESV)
11Moreover, the word of the LORD came to me: 12 "Son of man, raise a lamentation over the king of Tyre, and say to him, Thus says the Lord GOD:
"You were the signet of perfection,
full of wisdom and perfect in beauty.
13You were in Eden, the garden of God;
every precious stone was your covering,
sardius, topaz, and diamond,
beryl, onyx, and jasper,
sapphire, emerald, and carbuncle;
and crafted in gold were your settings
and your engravings.
On the day that you were created
they were prepared.
14You were an anointed guardian cherub.
I placed you; you were on the holy mountain of God;
in the midst of the stones of fire you walked.
15You were blameless in your ways
from the day you were created,
till unrighteousness was found in you.
16In the abundance of your trade
you were filled with violence in your midst, and you sinned;
so I cast you as a profane thing from the mountain of God,
and I destroyed you, O guardian cherub,
from the midst of the stones of fire.
17 Your heart was proud because of your beauty;
you corrupted your wisdom for the sake of your splendor.
I cast you to the ground;
I exposed you before kings,
to feast their eyes on you.
18By the multitude of your iniquities,
in the unrighteousness of your trade
you profaned your sanctuaries;
so I brought fire out from your midst;
it consumed you,
and I turned you to ashes on the earth
in the sight of all who saw you.
19All who know you among the peoples
are appalled at you;
you have come to a dreadful end
and shall be no more forever."
The third line of verse 16 in particular is similar to a verse in Revelation:
Revelation 12:9 (ESV)
9And the great dragon was thrown down, that ancient serpent, who is called the devil and Satan, the deceiver of the whole world— he was thrown down to the earth, and his angels were thrown down with him.
So, we have here two passages referring to the king of Tyre that seem to be contradictory as to whether this king is a man or Satan. I'll bet that this is similar to when Jesus rebukes Peter:
Matthew 16:23 (ESV)
23But he turned and said to Peter, "Get behind me, Satan! You are a hindrance to me. For you are not setting your mind on the things of God, but on the things of man."
Mark 8:33 (ESV)
33But turning and seeing his disciples, he rebuked Peter and said, "Get behind me, Satan! For you are not setting your mind on the things of God, but on the things of man."
Obviously, Peter is not Lucifer, but he certainly could have been greatly influenced by Satan. Similarly, the king of Tyre may have been a man AND been possessed or greatly influenced by Satan. Thus, the "king of Tyre" just might be both a regular human king and Satan.