  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 which should naturally
occur in a SSC scenario for a better understanding of the emission mechanisms,
especially at very high energies (VHE). Methods. We use simultaneous data from
a multi-wavelength campaign of Planck, Swift-UVOT and Swift-XRT telescopes
carried out in February 2010, as well as quasi-simultaneous data of WISE, Fermi
and H.E.S.S. 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 VLBI
extended 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 SED. We
can link the observationnal 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 such
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 via
inverse Compton processes.
