Ap Lib is one of the rare low-synchrotron-peaked blazars detected so far at TeV energies. This type of source is not properly modelled by standard one-zone leptonic synchrotron self-Compton (SSC) emission scenarios. The aim of this paper is to study the relevance of additional components that should naturally occur in an SSC scenario for a better understanding of the emission mechanisms, especially at very high energies (VHE). We use simultaneous data from a multi-wavelength campaign of the Planck, Swift-UVOT, and Swift-XRT telescopes carried out in February 2010, as well as quasi-simultaneous data of WISE, Fermi, and HESS taken in 2010. The multi-lambda emission of Ap Lib is modelled by a blob-in-jet SSC scenario including the contribution of the base of the VLBIextended jet, the radiative blob-jet interaction, the accretion disk, and its associated external photon field. We show that signatures of a strong parsec-scale jet and of an accretion disk emission are present in the spectral energy distribution. We can link the observational VLBI jet features from MOJAVE to parameters expected for a VHE-emitting blob accelerated near the jet base. The VHE emission appears to be dominated by the inverse-Compton effect of the blob relativistic electrons interacting with the jet synchrotron radiation. In this scenario, Ap Lib appears as an intermediate source between BL Lac objects and flat-spectrum radio quasars. Ap Lib could be a bright representative of a specific class of blazars, in which the parsec-scale jet luminosity is no more negligible compared to the blob and contributes to the high-energy emission through inverse-Compton processes.