When Love with unconfinèd wings Hovers within my gates, (1-2)
Love's wings are "unconfinèd," which suggests that there is some connection between powerful feelings (like love) and freedom. Perhaps freedom is simply a matter of loving somebody enough, or experiencing a similarly intense emotion.
When I lie tangled in her hair And fetter'd to her eye, (5-6)
"Tangled" and "fettered" are words of confinement. Here, though, the speaker imagines a type of confinement that is different from being in prison. This is his way of making the best of his situation, of imaging a type of imprisonment that is pleasurable.
The birds that wanton in the air Know no such liberty (7-8)
Birds seem really "free." We mean, they can fly, after all. Apparently, freedom is not just about being able to fly around in the sky, though, because the speaker claims he knows a type of freedom that trumps that ability.
When flowing cups pass swiftly round With no allaying Thames (9-10)
The "flowing cups" seem like a metaphor for freedom. First off, they flow, and they're also not diluted, not "confined" or "inhabited" by any sort water (the "allaying Thames").
When, like committed linnets, I With shriller throat shall sing The sweetness, mercy, majesty, And glories of my King; (17-20)
These lines mimic the speaker's confinement. Lots of letters are repeated (notice the alliteration of the words that begin with s and m), which suggests that—even on a formal level—the speaker's choice of letters is "committed" or "imprisoned" as well.
Stone walls do not a prison make, Nor iron bars a cage; (25-26)
If "iron" and "stone" don't make "prisons," what does? The speaker suggests that the only real prisons out there are ones people make themselves. The human mind is more powerful than strong building materials like iron and stone.
If I have freedom in my love, And in my soul am free, Angels alone, that soar above, Enjoy such liberty (29-32)
Lovelace basically says that he is like an angel. He suggests, almost, that one can experience the freedom of an angel (whatever that might be) by having freedom in one's love and being free in one's soul. This brings an important religious, or at least spiritual, dimension of freedom to the poem.