The increasing complexity of modern Integrated Circuits (ICs) leads to systems composed of various different Intellectual Property (IPs) blocks, known as System-on-Chip (SoC). Such complexity requires strong expertise from engineers, that rely on expansive commercial EDA tools. To overcome such a limitation, an automated open-source logic synthesis flow is required. In this context, this work proposes LSOracle: a novel automated mixed logic synthesis framework. LSOracle is the first to exploit state-of-the-art And-Inverter Graph (AIG) and Majority-Inverter Graph (MIG) logic optimizers and relies on a Deep Neural Network (DNN) to automatically decide which optimizer should handle different portions of the circuit. To do so, LSOracle applies k-way partitioning to split a DAG into multiple partitions and uses a to chose the best-fit optimizer. Post-tech mapping ASIC results, targeting the 7nm ASAP standard cell library, for a set of mixed-logic circuits, show an average improvement in area-delay product of 6.87% (up to 10.26%) and 2.70% (up to 6.27%) when compared to AIG and MIG, respectively. In addition, we show that for the considered circuits, LSOracle achieves an area close to AIGs (which delivered smaller circuits) with a similar performance of MIGs, which delivered faster circuits.