It makes little sense by itself. This phrasing (ab)uses artistic license to a great degree, so I doubt I can bring up a nearly literal translation that conveys the nuance.
Grammatically explained, the first part 凛として is "being dignified/frigid" (凛 is literally like "cold and contracted", and figuratively refers to "unapproachable stylishness"), an adverbial or continuative phrase, that requires another predicate either way. The second part 時雨 is "drizzle or shower in late autumn", a noun, obviously not a predicate. That's why this phrase is ungrammatical.
However, there is a poetic technique often employed in haiku, that cuts off the main predicate and places a noun phrase right beside it.
lit. the lake, being so vast and boundless, and one grebe
lit. With both the life and the death laid in heaps, the winter eggs
In these haiku, what the last nouns have to do with the rest is grammatically unspecified, because what should conclude the sentence is omitted. The composition is merely a device to achieve rhetorical effect of superimposing a scene to another, so the completeness of sentence is out of scope. The name 凛として時雨 is probably devised with those things in mind (時雨 is a traditional seasonal keyword 季語 in haiku, too).