A root in The Etymologies of the 1930s with no derivatives (Ety/SLUK).
Middle Primitive Elvish
lank
root. swallow
lak
root. swallow
sluk
root. swallow
There are more words but they are from Tolkien's earlier conceptional periods. Tolkien likely changed these words as he evolved the aesthetics and completeness of the languages. You may even find languages that Tolkien later rejected. Do not mix words from different time periods unless you are familiar with the phonetic developments.
Below: Tolkien's Late Period (1950–1973). These are from Tolkien's late conceptual period — his most settled forms of the languages. Prefer these over the earlier ones above when composing new text.
A root in The Etymologies of the 1930s glossed “swallow” with variant ᴹ√LANK and derivatives ᴹQ. lanko/N. lhanc “throat” (Ety/LAK¹, LANK), the latter an element in N. tarlanc “stiff-necked, obstinate” (Ety/TÁRAG). This last word was changed to S. tarlang in Tolkien’s later writings (PE17/92; RC/536), consistent with an earlier but rejected form ᴹ√LANG for ᴹ√LANK in The Etymologies (Ety/LANK).
In later writings, Q. lango/S. lang meant “neck” rather than “throat”, so it is tempting to retain ᴹ√LAK for “throat” and other swallow-words. But it would be very confusing to have such similar but unrelated words for “neck” and “throat”, so I recommend using the root ᴹ√SLUK for “swallow” instead, and Q. lango, S. lang for both “neck” and “throat”.