Most airliners carry a significant amount of cargo in the lower hold but on smaller aircraft the space is quite limited and we're talking about 100-200 kgs on something like a twin-otter if there is a decent pax load so its usually time sensitive stuff or urgent things like medicine. If there are not many passengers some airlines carry cargo in the passenger cabin but this is generally not officially permitted.
For most islands most of them get their supplies via ship, weekly or monthly but I suspect daily in the case of Lazarote as its quite near the mainland and the tourist industry is thriving.
Anilv