The Life Points payment of Gishki Photomirror is not a cost, it is part of the effect. Therefore, even if Spell Economics is active, you would pay Life Points and then perform the Ritual Summon.
You can pay attention to the text and if they have "," or ";" they are mostly a cost.
It's the same case with mausoleum of the emperor. That paying lp is part of effect to using it not the cost. Cards like cosmic cyclone, ties of the brethren, abyssal designator then they work with economics.
The key are the last words on Gishki Photomirror; Spell Economics makes allows you to not pay lp to ACTIVATE a spell, Photomirror makes you pay lp when it RESOLVES not when you ACTIVATE it.