Traditional digital implementations of neural accelerators are limited by high power and area overheads, while analog and non-CMOS implementations suffer from noise, device mismatch, and reliability issues. This paper introduces a CMOS Look-Up Table (LUT)-based Neural Accelerator (LUT-NA) framework that reduces the power, latency, and area consumption of traditional digital accelerators through pre-computed, faster look-ups while avoiding noise and mismatch of analog circuits. To solve the scalability issues of conventional LUT-based computation, we split the high-precision multiply and accumulate (MAC) operations into lower-precision MACs using a divide-and-conquer-based approach. We show that LUT-NA achieves up to $29.54\times$ lower area with $3.34\times$ lower energy per inference task than traditional LUT-based techniques and up to $1.23\times$ lower area with $1.80\times$ lower energy per inference task than conventional digital MAC-based techniques (Wallace Tree/Array Multipliers) without retraining and without affecting accuracy, even on lottery ticket pruned (LTP) models that already reduce the number of required MAC operations by up to 98%. Finally, we introduce mixed precision analysis in LUT-NA framework for various LTP models (VGG11, VGG19, Resnet18, Resnet34, GoogleNet) that achieved up to $32.22\times$-$50.95\times$ lower area across models with $3.68\times$-$6.25\times$ lower energy per inference than traditional LUT-based techniques, and up to $1.35\times$-$2.14\times$ lower area requirement with $1.99\times$-$3.38\times$ lower energy per inference across models as compared to conventional digital MAC-based techniques with $\sim$1% accuracy loss.