Per the initial question, you must leave the light in the level. You cannot remove the light and expect the level to retain the baked light information. As for attaching a “static” light to a character: that does not work, either. Once the character moves, the light is now moving and thus, “dynamic.” Dynamic lighting is not supported for HTML5.
If you have a static light that you are keeping in the level when packaging after building the lighting and this lighting is not showing up in the final HTML5 build, please start a new AnswerHub post, including precise repro steps, as that is a different issue than the one posted here. -Thanks