My friend still works at the same company (think PepsiCo, United Airlines, etc) they only asked for copy of L2 Visa, Marriage Cert, and Social Security, 
and we were advised by the lawyer who helped us file L visas that we did not need EAD. This lawyer was a former USCIS agent, and we believed what he advised
Aliens employment-authorized without specific DHS authorization
The following chart lists, by COA code, non-immigrants authorized to work in the U.S.without specific authorization from DHS. The alien’s I-94 showing one of the following COAs has employment authorization unless otherwise noted. The I-94 will not have the DHS employment authorization stamp and the alien will generally not have an EAD.
The visa of the principal alien generally shows the basis for the visa, e.g., “treaty trader” or an employer’s name, while the visa of a spouse or child may show an annotation that the person is a “dependent of the p.a.” (p.a. means principal alien).
For COAs displaying an asterisk (*), the principal alien, spouse, and child all have the same classification code.
In some instances, the husband and wife are principal aliens when the classification is E-1 and E-2.
When all family members have the same COA, ask the SSN applicant if he or she is the family member who is the principal alien, spouse, or the child of the principal alien.
For COAs displaying a double asterisk (**)(non-immigrant E-1, E-2, and L-2 classifications), the spouse is also authorized to work without specific DHS authorization.
When the E-1, E-2, or L-2 spouse applies for an SSN card and does not submit an EAD as evidence of employment authorization, he or she must submit, in addition to evidence of lawful alien status, evidence of a marital relationship to the principal E-1, E-2, or L-1 alien. The evidence of marital relationship between the applicant and the principal E-1, E-2, or L-1 alien is a marriage document. The marriage document must indicate the marriage occurred, either: 1) prior to admission to the U.S. as an E-1, E-2, or L-2 non-immigrant; or, 2) prior to extension or change of status to an E-1, E-2 or L-2 non-immigrant.
L-2** Spouse of an intra-company transferee.
The alien must submit either:
an EAD (Form I-766) showing “A-18” under Category; or
evidence other than an EAD that proves the L-2’s lawful alien status (e.g., I-94)and a marriage document as evidence that he or she is the spouse of the principal L1 Alien