The manifestations of the anomalistic and synodic lunar cycles in Arctic sea ice cover are examined in detail here
and here :
This graph puts them in a broader context. The annotations show approximate magnitude of the combined power of the peaks of the two triplets that are detailed above.
The other peaks indicated are harmonics of the annual cycle that reflect its deviation from a simple harmonic oscillation. In particular the sharp dip towards the September minimum. The spring-time maximum in ice cover showing more gradual change.
It is clear that the lunar signals are significant with respect to the faster changing parts of the annual cycle. The timing of these cycles contributes to whether a particular year has a more or less extreme minimum.
Any attempt to examine inter-annual variation in the timing or magnitude of summer sea ice minima or duration of the melting season need to take account of the presence of these cyclic effects.
This is rarely, if ever, done.