How can we test the lifespan of electrical components?
It is excellent to test your product like you describe but it is not the easiest way to provide a rationale for the lifespan. The following method is the one I follow in the medical devices industry :
Step 1 :
The more important thing you first need to have is a good definition of the use cases your electronic components will face. You mention a target lifespan of 1 to 5 years, but will the components be always powered during this period for example (LCD working only 10 hours a day)? By making this you will extract a list of the minimal ON time you must ensure for each electronic parts of your design.
Step 2 :
For each component, investigate the datasheet and look for the mean time between failures (MTBF) or the mean time to failure (MTTF) and compare it with your use cases. In this example, if you look at page 11 you will find a lot of useful information. The manufacturer did it well, so don't waste time and money by redoing tests :

Step 3
Well, the previous example is a nice one but you will face laconic datasheets where you will not find the information you are looking for. In this case, before doing tests you should contact the manufacturer and ask for the information. Sometimes you will be able to obtain useful information that was not made public in the datasheet (I still don't know why but it can happen).
Step 4
If in the end you were not able to find any information but you definitely need it (required for a certification or as you mention to know where it is more likely to fail), you will have to do the test. In my company there is a whole department dedicated to this so you should not underestimate the work and the money it can involve. We have a lot of tools like programmable power supply, programmable loads, expensive probing tools to continuously monitor changes, .... The merging of all the data requires a very good knowledge of statistical methods. Also, the derating of components when subjected to high temperature, high humidity levels (among others) is a complex domain and should be handled with care. But definitely if you reach this step, I strongly recommend to look for experts in this domain. They will advise you according to your needs, your deadlines and your budget. Most engineering consulting companies provide this service.