Where applicant will manage company department and supervise low level employees, is she eligible for L1-A or E-2 visa?

Possibly, but much more information would be required to make that determination.

L-1A and E-2 visa are two separate categories, one is intra company transfer or establishing a new bussiness for the company overseas and E-2 is investment visa for Treaty countries with USA. You need to be specific in your question and better contact an attorney to discuss which will suit you

L-1 and E-2 visas are extremely complex and require a thorough business plan. There is no one-size-fits-all business plan or immigration strategy for these types of visas. Much will depend on the capital investment, the location, the experience of the owners/managers, the type of business, etc. is never a substitute for legal advice. An attorney should be hired for this type of case.

You have provided limited information in your scenario. Possibly the L-1 may be applicable if the individual qualifies by complying with all of the requirements from the federal statute and the regulations. Additionally, the petitioning employer has to fulfill other requirements. The E-2 is another classification of visa that has different requirements.