There can be issues ofcourse. There is no direct guidance and no one can predict what will happen at POE interview. But if you could establish through your husbands confirmed tickets that he is going to be soon joining you, they may let you in. Why not speak to your attorney who filed L-1A!
You will not be allowed to enter in L-2 if your husband is not maintaining L-1 status or with you at the airport. The POE Officer may let you enter on B-2 if you have that visa.
This response is general in nature and cannot be construed as legal advice, given that not enough facts are known. Any comments offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship. You are encouraged to seek independent and private counseling for a complete review of your case.
Since the L2 status is dependent on the L1 having status, You may have issues entering the US. in L2 before the L1 arrives.
Attorney Robert Brown's (former INS Director, 1972-99) reply to your question is general in nature, and does not constitute legal advice as all facts are known to him. For specific advice or representation you should retain an attorney experienced in immigration law. Mr. Brown's reply on AVVO does not create an attorney/client relationship not constitute legal advice.