As you noted, glaucophane and lawsonite are typical meta-mafic blueschist facies minerals (high P; low to mod T), but epidote and chlorite have wider stability fields, although they're most typical of greenschist facies (low to mod P; low to mod T), and below. So glaucophane+lawsonite rocks don't usually grow new epidote and chlorite with increasing grade (if they're going to higher P and/or T; the "prograde" path), but rather these latter minerals would more typically form as the blueschist is decreasing in grade (the "retrograde" path, going down in P and/or T), perhaps leaving some unreacted relict glaucophane and/or lawsonite behind.

An alternative scenario is that some earlier epidote+chlorite from the initial alteration of the original rock can also remain as relict minerals as the rock moves into the higher-P blueschist facies, so one has to carefully study the textural relationships among the minerals to figure out if you're looking at a "clockwise" P-T path (if on an X-Y plot you assign the +Y axis as increasing P and the +X axis as increasing T, then a clockwise path has rocks that go up in P first, then increase in T, then decrease in P, and finally decrease in T) or a "counterclockwise" P-T path (where rocks go up in T first, then up in P, then down in T, and finally down in P). These paths are very simplified of course, but this gives you a rough idea that at any specific point in P-T space for a given bulk composition, a set of minerals will be stable, and as the rock moves into other P-T regimes, the old minerals react out and new minerals form. When reactions are incomplete, relict minerals from earlier points along the P-T path are sometimes preserved. So you may have relict blueschist lawsonite with a superimposed retrograde veinlet containing epidote, the latter which could have formed during the cooling and decompression path.

If your rock was once in the eclogite facies (high P, high T), there may even be relict eclogite facies minerals preserved. Since eclogite facies minerals are largely anhydrous (in particular omphacite and garnet [but note garnet is common in mod-P facies too]), they tend survive the retrograde path well because because there's often little to no H₂O initially around to facilitate back-reactions. By the way, the epidote group minerals clinozoisite and zoisite in particular are also quite happy in fairly high-P rocks, so it could also be that your "epidote" might be more aluminous than you think and may in fact be part of the stable higher P assemblage rather than a retrograde phase.

I can't quite discern the specific mineral relationships from your photos, but hope this general overview helps in your understanding of your rock.