Who would own my design?

This comes up regularly where technologies are starting to overlap in ways not previously envisioned by the parties. Your employer may not consider "theatrical lighting design" as part of "your job" until the first time they are asked to send you for that. You then have several options: go with the flow, get paid, let the company "own" whatever you were paid to do for them; stop working for them and take the job yourself; or (perhaps) turn it into a new opportunity for your employer by showing them how you can lead them into a new and profitable development.

I have counseled people to consider making it a proposal to the company whereby they put the creative person "in charge" of developing the new area, or else deny any interest (in writing) in owning the types of work emerging from the venture. In other words, if you think you could do it on your own, and you want them to release you (from their work for hire ownership), now's the time. If you want to HELP them see how valuable your works can be in your specialized field, now's the time.

Just my two cents. Your local employment-law counselor may have a very different view of things.

In general the creative work a full time employee does in the course of their employment falls under the statute "Work for Hire" or "Work Made for Hire" and all rights to that work belong to the employer. In a freelance situation all rights to creative work remain with the author of the work unless there is a specific signed, written agreement otherwise.

When you work for a company and they send you to do work for a client, the company owns the work you do. That's the tradeoff for having a job.

Unless your design is copywritten/trademarked by you or your employer, neither you or your employer or anyone else owns the design. But it would be reasonable for the company to claim credit because the company was hired to do the job, not you individually.

The work you do as an employee of the company belongs to them. Anything else you do doesn't.

As the employee, your work is owned by the company.

If the company is hired to do this job, and they assign you to do the job, then they own your work products. They would get credit because they provided their employee (you). If you want things to work out differently, then you are going to need a special agreement with the company.