Can I file a lawsuit if my e-cigarette caught on fire?

Yes.  If your e-cigarette caught on fire, you can sue the manufacturer, distributor and/or the retailer of the device or its components based on a theory of product liability (described above).  In California, there is a two year time limit, known as the statute of limitations, to file this type of lawsuit.

One aspect of a product liability claim is demonstrating that you used the product in a reasonably foreseeable way. Manufacturers are required to anticipate how the average consumer will use (or misuse) a product.  While it is usually not possible to completely eliminate the potential for harm, manufacturers must take reasonable steps to reduce the potential for harm.  This may include providing adequate warnings about how to use the product, designing the product to increase safety, or other steps.

As long as you used your e-cigarette in a way that a manufacturer could have reasonably foreseen, then you will meet this element.  For example, if your e-cigarette caught on fire while charging, this is a foreseeable use of the product — because you have to charge the device in order to use it.  However, if it caught on fire because you left it on the stove and the heat from the oven caused it to ignite, then this is not likely a reasonably foreseeable use of the product.