Large gains in strength and ductility are of little significance if the material’s anisotropy is high. Therefore, improving the mechanical properties and reducing the anisotropy of Al alloys obtained by additive manufacturing is a topic of growing interest. This manuscript examines the effect of distinct heat treatments on the mechanical, anisotropic, and microstructural behavior of a hypoeutectic, almost eutectic, AlSi11Cu alloy obtained by laser powder bed fusion (L-PBF). The microstructural characterization revealed an Al matrix surrounded by a Si-rich network, forming a coral-like pattern with a heterogeneous combination of columnar and equiaxed grains. The texture indicated that the columnar grains were preferentially oriented towards the building direction with strong Cube and Goss components. Different strength-ductility ratios were obtained following the annealing and solution heat treatments at different temperatures (200 °C–550 °C) with a holding time of 1 h. In terms of grain size and dislocation density, no significant changes were found in the microstructure, suggesting that grain size and dislocation strengthening mechanisms are not highly affected by the heat treatments. In addition, the Si-enriched network remained interconnected until 300 °C. At higher temperatures, this interconnection was lost, giving rise to large Si particles depleting the Si content in solid solution in the Al matrix. Digital image correlation maps revealed that deformation fields were more homogeneous when the cellular structure disappeared. The visco-plastic self-consistent model showed that when applying the load at 30° in the building direction (BD), the largest tensile strength was generated, whereas the lowest strength was obtained when the load was parallel to the BD. Heat treatments for 1 h holding time were found to be efficient in reducing the Lankford coefficients dispersion, suggesting improvements in formability and reducing the alloy’s planar anisotropy. These results revealed that annealing up to 400 °C or higher temperatures followed by water quenching leads to good strength and ductility ratios while reducing anisotropy.