It can be inferred that the effect of the poet using the phrase "lap dog" in reference to the speaker is such that it creates a sarcastic tone.
Sarcastic people say or do the reverse of what they truly intend in order to criticize or offend someone.
Hence, by stating that he would never be a lapdog licking dirty feet is actually a sarcastic reference or statement.
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Full Question:
Read the lines from "Lone Dog."
I'll never be a lap dog, licking dirty feet,
A sleek dog, a meek dog, cringing for my meat,
Not for me the fireside, the well-filled plate,
But shut door, and sharp stone, and cuff, and kick, and hate.