You are not entitled to a free lawyer to help you to write the initial application. You can hire a lawyer to do that or write the application yourself.
If your application is admissible and communicated to the Slovakian government, you may ask the Court for legal aid. You will have to find the lawyer yourself and pay for his/her services initially. The Court will only provide a limited amount of money for the services of your lawyer at a later stage of the proceedings. The amount it pays will be determined by the Court itself. Usually it covers the preparation of the documents necessary for the proceedings and correspondence with the Court. However, you have to be aware that the amount given by the Court may not cover all the costs of your lawyer’s services.
Remember that the Slovakian government does not have a duty to provide you with a lawyer. Neither the Slovak National Centre for Human Rights nor The Public Defender of Rights, which are independent institutions established by law have duties or competence with regard to the complainants.