An opinion: your Liechtenstein residence status (L) is not relevant to the Swiss authorities. It would be no different than if you held a temporary work/ residence permit in the Netherlands or some other EU/EFTA country and wanted to move to Switzerland for work as a third-country national.
The Swiss Authorities Online (ch.ch) says this about third-country nationals working in Switzerland:
"Working in Switzerland as third-country nationals
If you are a third-country national who has been offered a job in Switzerland, your prospective employer must submit an application to the cantonal immigration or labour market authorities. If the application is accepted, it will be forwarded to the State Secretariat for Migration (SEM) for approval. The SEM will then notify the parties and the cantonal authorities of its decision, but this decision does not constitute authorisation to enter Switzerland.
If you require a visa, the cantonal migration authorities will send a visa clearance certificate via e-mail to the Swiss diplomatic/consular mission in your home country. You can then obtain the visa there. Within 14 days at the latest of your arrival and before taking up employment, you will need to register with the communal authorities in the place where you are living and only then can you begin work.
The following requirements apply to employment of third-country nationals:
- Authorisation is only granted if established quotas have not been used up.
- Third-country nationals may only be hired if no one with equivalent qualifications can be found in Switzerland or in an EU/EFTA member state.
- Only managers, specialists and other qualified workers will be admitted. “Qualified workers” are primarily the holders of higher education qualifications (i.e. from a university or university of applied sciences) who also have specific technical expertise and several years of professional experience. Integration criteria will also be taken into account when issuing residence permits: ability to adjust to a new occupational and social environment, language skills and age.
- Salary and working conditions must also be equivalent to those that apply to Swiss inhabitants."