The phrase "used to reconstruct language families using the comparative method" is not literally meaningful, since you can reconstruct linguistic forms or you can make hypotheses about the grouping of languages into families, but you can't reconstruct a family. I think you mean "used in the reconstruction of an earlier stage of a language". As example of that would be the derivation of long vowels in proto-Indo-European from the loss of earlier laryngeals. That would be a case of compensatory lengthening as Jlawler mentions. In addition to vocalic merger (with or without there having been an intervening consonant), there are various prosodic causes. The Norwegian case, which has a parallel in North Saami, involves a change in syllabification where VCCV could be parsed as V.CC or VC.CV, and the change is from non-branching onsets to branching onsets with no coda i.e. VC.CV -> V.CCV. A frequent instance of that is lengthening of vowels before NC clusters in Bantu. Another very common one is stress-related: stress may be assigned to some position, and that causes vowel lengthening (a number of Bantu languages, Mohawk, etc.). A third context for lengthening is "minimality" related, where monosyllables (typically) have to lengthen their vowel because every word has to have at least two moras (various Bantu, Arabic dialects).
Numerous historical questions are associated with lengthening, such as "does lengthening by such-and-such process require pre-existing phonemic vowel length", but you'd have to be more specific about what connection between lengthening and reconstruction you're asking about.