Is there a way to specify how many words need to follow the last natural line-break in a paragraph?

Not yet. Is the paragraph justified or unjustified?

The paragraph is unjustified.

For unjustified paragraphs Prince will use the standard "greedy" line-breaking algorithm used by web browsers, fitting as many words as possible on each line with equal-sized spaces between words. This gives no control over the number of words appearing on the last line of a paragraph, which depends purely on chance.