Can I sue my present lawyer for double dipping, receiving money from me and workers comp.

I am not sure what you are asking.  You have a fee agreement with the lawyer.  usually, a legal fee for workers comp is 20% of what is collected.  I am not sure what you mean by double dipping.  Why are you saying the lawyer is double dipping?  I think that you need to get a statement from the lawyer itemizing all the fees and costs that the lawyer has taken.  You should then  review the retainer agreement to determine whether there is justification for the money that the lawyer is taking as a fee.  You should take these documents to a lawyer for an opinion before you accuse someone of a serious thing like double dipping.

If you feel like your attorney is being compensated unfairly, the first thing that you should do is to take a look at the retainer agreement that you signed when you hired him/her to represent you.  The rules of ethics require an Attorney to have written agreement that explains the fee arrangement.  Thus, this agreement should outline the attorney's compensation.  It is possible that you agreed on a mixed fee/contingency arrangement, whereby you would pay the attorney a fee and he would be entitled to a percentage of your judgment/settlement.  Or, it is also possible that the agreement does not entitle the attorney to any percentage of a settlement/judgement.  Nevertheless, you need to start by looking at that agreement.  

With respect to your question of whether you can sue him/her, if you did you would probably only be able to recover damages in the amount that he/she has compensated him/herself with monies that were supposed to go to you, assuming of course that he/she is compensating him/herself in violation of your written fee agreement.  In addition to "suing" your lawyer, it is also possible for you to file a grievance with your state legal ethics board/bar association if you feel that your attorney is being compensated unethically.  If the grievance is successful, the penalties may involve the attorney being ordered to repay the money and/or may include penalties on his abilities to practice law.

Regardless, if you feel that you are being treated unfairly by your present attorney you should consult with different skilled workers compensation attorney immediately.