The way I have understood your question is that you as a facilitator of LSP activities are being asked by a client to use LSP to support an interview process. I think it would be helpful to be careful with your terminology.
A facilitator-led interactive process in which one participant builds metaphorical models with LEGO pieces and then tells a story about them may share some features with LEGO Serious Play, but is not necessarily LSP.
If you have an interviewer and an interviewee building their ideal candidate / ideal job simultaneously, that might still not be LSP per se, although it might be a useful skill building exercise.
On the other hand if you have a representative from the client’s HR department, the functional line manager to whom the candidate would report, a potential peer/colleague of the candidate and the candidate themselves, then you could embark on something like this:
1. Build an individual model of how you perceive the job (depending on the role of the participant, they will build the job as described in the announcement or how they experienced someone else performing it or they might just build a combination of skills that are currently missing.
2. Build a shared model of this job
3. Build individual model of the company’s corporate values and working environment. It’s always interesting for staff within a firm to hear how potential candidates perceive that firm from the outside and of course it is important for the candidate to understand what is the environment in which they would be working.
4. Enhance the shared model of the job to reflect the values and environment.
5. Build individual models of key actors and factors that have an impact on the job.
6. Place those actors and factors around the shared model.
7. Build the connections between actors, factors and the job.
You could go on to do scenarios and what-ifs, but you would probably be running out of time.
Hope this helps.
All the best,