GVK
You know what? I don't know. You shouldn't ask people of the internet if it's an earnest, important issue to you. Swami Amritananda gave me some mantras. Mantras he didn't specifically give me, he also gave me, because he said over and over. By hearing my voice recite this mantra, you have had initiation into this mantra. Her Holiness Sri Annapurnambaji also gave me some mantras.
I feel comfortable that I can do any of the practices here at Devipuram. I have had other dikshas which said, "This is the ultimate diksha; you do not ever need another diksha after this."
One should know that there is a difference between a mantra diksha and a stotra/namavali/ritual diksha. The importance of many diksha happens to be that they express the lineage.
One doesn't need a Trishati diksha. Only if it is a special version. You were correct. Many of the TripuraTallika documents were transliterated from what I understand, during the Monsoon on 2008 when Devipuram was decimated. The persons there took it upon themselves to do fine transliterations of special Sri Vidya practices. The practices were for the Devipuram people by the Devipuram people in attendance during that time.
In this way, all Devipuram people have had diksha to practice any of the Tripura Tallika documents.
But if one is a Lalita devotee then one should feel comfortable reciting her stotrams. Who but you are they for? They are for you, Friend. By Her Grace, wait no longer, and recite, get to know The Goddess. There is little time. By Kali, the time to practice is now.
Please begin and stop waiting for someone to give you permission. You are the Upaguru. Swami Amrita would say. Begin already! Wouldn't he? What do you think he would say?