Fluorescence lifetime imaging (FLI) has been receiving increased attention in recent years as a powerful diagnostic technique in biological and medical research. However, existing FLI systems often suffer from a tradeoff between processing speed, accuracy, and robustness. Inspired by the concept of Edge Artificial Intelligence (Edge AI), we propose a robust approach that enables fast FLI with no degradation of accuracy. This approach couples a recurrent neural network (RNN), which is trained to estimate the fluorescence lifetime directly from raw timestamps without building histograms, to SPAD TCSPC systems, thereby drastically reducing transfer data volumes and hardware resource utilization, and enabling real-time FLI acquisition. We train two variants of the RNN on a synthetic dataset and compare the results to those obtained using center-of-mass method (CMM) and least squares fitting (LS fitting). Results demonstrate that two RNN variants, gated recurrent unit (GRU) and long short-term memory (LSTM), are comparable to CMM and LS fitting in terms of accuracy, while outperforming them in the presence of background noise by a large margin. To explore the ultimate limits of the approach, we derive the Cramer-Rao lower bound of the measurement, showing that RNN yields lifetime estimations with near-optimal precision. To demonstrate real-time operation, we build a FLI microscope based on an existing SPAD TCSPC system comprising a 32x\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\times $$\end{document}32 SPAD sensor named Piccolo. Four quantized GRU cores, capable of processing up to 4 million photons per second, are deployed on the Xilinx Kintex-7 FPGA that controls the Piccolo. Powered by the GRU, the FLI setup can retrieve real-time fluorescence lifetime images at up to 10 frames per second. The proposed FLI system is promising and ideally suited for biomedical applications, including biological imaging, biomedical diagnostics, and fluorescence-assisted surgery, etc.