Many Linguistics textbooks classify the "l", the lateral liquid, as +continuant. This was certainly the case in my introductory textbooks. In reality, though, the situation is not so simple. In certain situations, the lateral liquid functions more as an obstruent such as a plosive. Let's take a look at a few examples.
In Spanish the voiced dental plosive "d" is an interdental fricative between vowels and word-finally. These can be classified as less perceptually salient positions, therefore making them weak. The realization of the "d" as a fricative can be considered the result of a weakening process. Where it is preceded by a lateral, it is realized as a plosive. This is the case in "caldo", the word for broth. In the case of a preceding alveolar trill, however, the "d" is a fricative. This is so in "cerdo" meaning pig. In these cases the lateral clearly functions as -continuant, unlike the trill which is +continuant.
In many varieties of English the voiceless and voiced alveolar plosives are flapped in an intervocalic position in which the preceding syllable is stressed, i.e., "city", "letter", "metal", "medal". Flapping also occurs if the preceding segment is an alveolar approximant as in "party". If the preceding segment is a lateral, flapping does not occur as in "faulty". Again the lateral here functions as -continuant.
In many varieties of British English, the alveolar approximant is deleted or realized as a schwa syllable finally when there is no following vowel. Examples are "here", "father" and "faster". With a syllable-final lateral, vocalization may occur (this is the case in a few dialects), but never deletion. This would appear to be a feature associated with a sound that is +continuant more so than -continuant.
In the speech of many Brazilian Portuguese speakers, the alveolar trill is often deleted syllable- finally when no vowel follows. This is so in "falar" (to speak) and "pensar" (to think). However, the lateral, though it may vocalize, never deletes. This is again a quality associated more with sounds that are +continuant than -continuant.
Consonant clusters also provide good clues as to the nature of the liquids. English allows syllable-initial .tr as in "train" but not .tl. This is the pattern English has with respect to plosives which never occur in syllable-initial sequences. Here the lateral patterns as a -continuant. English allows the syllable initial sequence .sl as in "slow" but not .sr. (The word "Sri Lanka" is a possible exception but note that many pronounce the first segment as a voiceless alveopalatal fricative usually spelt in English as "sh"). The sequence .sr does not occur and neither does a sequence of two fricatives. That the sequence .sl can occur shows that the lateral patterns here the same as a plosive. Fricative plosive sequences can occur such as .st, .sp and .sk. This provides more evidence that the lateral also functions as a -continuant here.
It may be so that the alveolar lateral tends to function as a continuant but plenty of examples can be provided to counter this. The evidence is clear: the lateral often patterns as an obstruent and can thus often be analyzed as a -continuant. Perhaps a better classification of the alveolar lateral is that of +/- continuant.