Like almost every answer to a cancer question, the answer to the question of whether lymphoma can be caused by asbestos exposure is ... nobody can say yes or say no with any absolute certainty. However, conclusions have been reached on the subject, and they appear to be headed toward a consensus.
Asbestos is a term used for six naturally occurring minerals that have been mined by humans for many hundreds of years because of its abundant practical properties -- notably, its ability to absorb sound, resist heat, and be really cheap to extract and process. Another quality of asbestos is its form: it is made of very long, fibrous crystals.
When pulverized or otherwise airborne, asbestos fibers present a significant health threat to humans. Prolonged exposure -- specifically, prolonged inhalation of asbestos fibers -- can cause a fatal form of lung cancer known as mesothelioma, along with other respiratory problems. It is not necessary to work around asbestos to inhale the fibers; one only needs to live with or be around someone who works near the fibers to be at risk.
Because of the nearly undeniable link between asbestos exposure and lung cancer, and because of several case studies that would appear to lend some credence to the notion of a link between asbestos and lymphoma, the question of whether a link can be found or proven has been the subject of several research projects and several dozen epidemiological studies.
The results rather strongly suggest that asbestos exposure is not a cause of lymphoma. These results include a 2001 review of the epidemiological literature, an even larger 2002 review of the epidemiological literature, and a 2010 multicenter case-control study.
Keep in mind that determining the cause of most cancers on a case-by-case basis is, if not entirely impossible, then certainly next to entirely impossible, so the only evidence that can be used to draw these kinds of links and associations between exposure to a certain element and the incidence of a cancer is epidemiological evidence. In fact, the only hard evidence that cigarette smoking causes lung cancer comes not from some laboratory smoking gun (forgive the pun) but from the overwhelming epidemiological evidence (stacks and stacks of it).