This question you ask hits upon a complex point in criticism of Wyatt's work. Critics generally agree that Wyatt spoke in his poems with a duplicity that veiled a social or political or cultural truth behind a simpler poetic truth. For instance, Wyatt's poem “Goo burnyng sighes” [“Go Burning Sighs”] on the surface, or literally, is a poem about the poetic speaker's inability to persuade his beloved through
pitefull plaint & scalding fyer
that oute my breast doth staynably stert.
[pitiful complaint and scalding fire
that out my breast does strainably start].
Yet the figurative meaning is a veiled and concealed pronouncement that being earnestly truthful and honest at Henry VIII's court is ineffectual (Hobson/Crewe)
for trueth & faith in her laide apert
Alas I cannot therefor assaill her
[for truth and faith in her is laid aside
Alas, I cannot therefor assail her]
The poem is a veiled statement that "craft & art" are needed for speaking the council of truth and honesty at court:
I must goo worke I se by craft & art
[I must go work I see by craft and art]
This theory of veiled, concealed, figurative meaning in Wyatt's poems applies in very much the same way to "My Lute, Awake!." On the surface, the literal meaning is that a suitor for a woman's love has given up, thrown in the towel, so to speak, and will henceforth quit trying to win his beloved's love because she not only rejects him, she also scorns him:
Proud of the spoil that thou hast got
Of simple hearts thorough Love's shot,
Yet the concealed, veiled, figurative meaning is that at court, Wyatt is rejected and scorned by King Henry VIII when he attempts--through craft and art, or tact and diplomacy--to council truth and honesty; he is rejected and scorned when he attempts to accomplish what he has begun: “And ended is that we begun; ….” Just as the suitor in the literal understanding will give up trying to win the lady's love, so will Wyatt give up trying to persuade Henry VIII to wisdom as he, Wyatt, had begun to try to do:
The rocks do not so cruelly
Repulse the waves continually
As she my suit and affection:
So that I am past remedy,
Whereby my lute and I have done.