Yes. Clarity is worth the trouble of more punctuation.

Let’s say you quote the following two lines of poetry:

He had forty-two boxes, all carefully packed,

With his name painted clearly on each:

To make it clear to readers that you are quoting the beginning of one line and the ending of the next, use ellipses to replace omitted words and a slash to indicate that one line ends and another begins:

The poet writes, “He had forty-two boxes, . . . / . . . his name painted clearly on each.” 

The following treatment would not make that clear:

The poet writes, “He had forty-two boxes, . . . his name painted clearly on each.”

Note also that when a whole line is elided, you need to use a double slash. For example, let’s say you quote from the following poetic passage:

The loss of his clothes hardly mattered, because

He had seven coats on when he came,

With three pair of boots—but the worst of it was,

He had wholly forgotten his name.

Your quotation might appear as follows:

The poet writes, “The loss of his clothes hardly mattered,  . . . // . . . but the worst of it was, / He had wholly forgotten his name.”

You also have the option of setting your example as a poetry extract:

The loss of his clothes hardly mattered,  . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . but the worst of it was,

He had wholly forgotten his name.

Work Cited

Carroll, Lewis. The Hunting of the Snark. Literature.org, 24 Oct. 1995, literature.org/authors/carroll-lewis/the-hunting-of-the-snark/.