When arranged in a crossbar configuration, resistive memory devices can be used to execute Matrix-Vector Multiplications (MVMs), the most dominant operation of many Machine Learning (ML) algorithms, in constant time complexity. Nonetheless, when performing computations in the analog domain, novel challenges are introduced in terms of arithmetic precision and stochasticity, due to non-ideal circuit and device behaviour. Moreover, these non-idealities have a temporal dimension, resulting in a degrading application accuracy over time. Facing these challenges, we propose a novel framework, named LionHeart, to obtain hybrid analog-digital mappings to execute Deep Learning (DL) inference workloads using heterogeneous accelerators. The accuracy-constrained mappings derived by LionHeart showcase, across different Convolutional Neural Networks (CNNs) and one transformer-based network, high accuracy and potential for speedup. The results of the full system simulations highlight runtime reductions and energy efficiency gains that exceed 6×, with a user-defined accuracy threshold for a fully digital floating point implementation.