No, you do not need a lawyer or any other representative for an EU trademark application. You can apply directly in your own name. The web site of the EUIPO (Intellectual Property Office of the Europena Union) provides for a guided application even understandable for non-layers. However, please note the following if your company does not sit in the European Union nor has branch in the EU. Then, the EUIPO might request you in the course of the further application proceedings to name a representative located within the EU.