  A search for new heavy particles that decay into top-quark pairs is performed
using data collected from proton-proton collisions at a centre-of-mass energy
of 13 TeV by the ATLAS detector at the Large Hadron Collider. The integrated
luminosity of the data sample is 36.1 fb$^{-1}$. Events consistent with
top-quark pair production are selected by requiring a single isolated charged
lepton, missing transverse momentum and jet activity compatible with a hadronic
top-quark decay. Jets identified as likely to contain $b$-hadrons are required
to reduce the background from other Standard Model processes. The invariant
mass spectrum of the candidate top-quark pairs is examined for excesses above
the background expectation. No significant deviations from the Standard Model
predictions are found. Exclusion limits are set on the production cross-section
times branching ratio for hypothetical $Z'$ bosons, Kaluza-Kein gluons and
Kaluza-Klein gravitons that decay into top-quark pairs.
