Most of the lancets in hospitals or clinics are single use - where the syringe or the lancet is actually disabled after use; those type actually prevent re-use. But, as an RN, I know people in their own homes don't always do (and don't always need to do) the same as is done in the hospital.
Re-use of lancets and syringes is a controversial subject. Some resources say not to re-use at all because of dulling and the chance of infection. Some (like the
American Diabetes Association) suggest not doing it, but recognize that many people do re-use without a problem.
The big things you need to worry about are person to person transmission (which is not a concern for reuse of your own equipment on yourself) and skin organisms being brought into the body by the lancet going thru the skin. So cleaning the skin and cleaning hands before doing a procedure is good practice.
Another thing to think about is the situation. A diabetic who has good control and seldom gets an infection is a much better choice to reuse equipment than someone who is either in poor control or has frequent infections.
If you DO choose to re-use, be aware that alcohol is a disinfectant, not a sterilizing agent and you don't want to put alcohol inside the needle. Most of the information about re-use of lancets and syringes suggest NOT using alcohol on either of them because they degrade the metal, remove the coating on the metal and make the needle or lancet dull faster. As has already been mentioned, it's usually recommended not to clean the lancet and just leave it in the lancing device. That is safest in terms of not injuring yourself with it and also not soiling it while taking it out. Of course, if you think that the lancet or the needle point have come into contact with something, you would discard it.
This site has some guidelines for re-use that look common sense.
BD (one of the manufacturers) has some
scary information about re-use of syringes from the point of view of needle damage.