-- Render to texture
As Megalomaniak said, render to texture is supported.
-- Lens flares
Not sure. Probably possible, but someone who knows more about the graphic capabilities of Godot probably knows better than I do. Worst case you could write your own in the source code (and then everyone can benefit)
-- Depth of field
Totally possible in Godot 3 and is included by default as a post process effect. I'm not sure if it's possible in Godot 2, but it might be. I haven't used Depth of field in Godot 2, but I have in Godot 3
-- Water plane
A water plane is doable with custom shaders. I would suggest doing it with either screen space reflections, or reflection probes. Screen space reflections and reflection probes are only available in Godot 3. You could write a shader for water planes in Godot 2 or Godot 3.
-- Decals
There is currently no support for decals in Godot by default. Decals are going to be added sometime in the future. I think it is planned for Godot 3.1.
-- Mipmapping
I don't know. There is mipmapping options for textures, but outside of that I have no idea. I've never used Mipmaps (to the best of my knowledge)
-- LOD
I have never used LOD, but Godot does support LOD. I saw a video for on LOD for Godot 2 and I assume Godot 3 also has LOD.
-- Is lighting and shadow shader based
Yes. Everything is done with shaders, with a few minor exceptions (probably. I don't know, but everything I've seen in the source code for graphics seems to be done with a shader).