See p. 3 of "Interpreting the Differences Among LSMEANS in Generalized Linear Models" by Robin High.
Briefly, the blue lines represent pairs of groups whose mean differences are significantly different from zero. (That is, the means are sig diff from each other.) The red lines represent pairs that are NOT significantly different from zero. In your example, the mean difference between the NI and PS groups are not sig diff. Similarly, the mean difference between the NI-LS groups and the LS-PS groups are not sig different. The other pairwise comparison of means are significantly different from each other.
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