Disclaimer: The materials provided below are informational and should not be relied upon as legal advice.
What licenses are you interested in checking? Most professional licenses are public and may be confirmed online or at the government agency's office. Some web links are provided below for your reference. You should consult your own lawyer to protect your legal rights.
You could ask the City of Los Angeles Finance Department, who adminsters LA business licenses, to see if they'll give out information about other licensees: http://www.lacity.org/finance/finH.cfm
And of course you could ask the person you're interested in.
Finding out a person's use of a fictitious business name requries you to know the name they're using, and then you could request copies of their DBA forms from the County recorder: http://www.lavote.net/Clerk/Business_Name.cfm
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.