It doesn't seem to be the culling, as I tried modifying the values of glCullFace and enabling/disabling it.
I do use alpha values in the lines for testing purposes.
Here is my render code:
GL11.glPolygonMode(GL11.GL_FRONT_AND_BACK, GL11.GL_LINE);
GL11.glEnable(GL11.GL_BLEND);
GL11.glBlendFunc(GL11.GL_SRC_ALPHA, GL11.GL_ONE_MINUS_SRC_ALPHA);
GL11.glEnable(GL11.GL_DEPTH_TEST);
GL20.glUseProgram(program.getId());
model.render();
GL20.glUseProgram(0);
GL11.glDisable(GL11.GL_DEPTH_TEST);
GL11.glDisable(GL11.GL_BLEND);
P.S. I could post the full code if needed