I want to come to the Republic of Lithuania for less than 3 months.
If you intend to stay in Lithuania for up to 90 days in any 180-day period, it is sufficient for you to have Schengen visa (if you are not subject to visa-free regime).

I want to visit the Republic of Lithuania for a short time (less than 90 days).
If you intend to visit the Republic of Lithuania for a maximum of 90 days within any 180 days, you may enter under the visa-free regime if you are subject to the visa-free regime or
with a valid Schengen visa if you are not covered by the visa-free regime.

How do I apply for a new temporary residence permit?
First, you have to fill in an application for a new temporary residence permit electronically using the Lithuanian Migration Information System.

I want to change the employer or a job function with the same employer. What should I do?
An foreigner is allowed to change the employer or a job function with the same employer during the validity term of the possessed temporary residence permit.

You can apply for permission to change employer no sooner than 6 months after the date of issue of the temporary residence permit. Is it true?
Yes.