In principle, the most straightforward method of estimating the Hubble constant relies on time delays between mirage images of strongly-lensed sources. It is a puzzle, then, that the values of H0 obtained with this method span a range from 50 - 100 km/s/Mpc. Quasars monitored to measure these time delays, are multi-component objects. The variability may arise from different components of the quasar or may even originate from a jet. Misidentifying a variable emitting region in a jet with emission from the core region may introduce an error in the Hubble constant derived from a time delay. Here, we investigate the complex structure of sources as the underlying physical explanation of the widespread in values of the Hubble constant based on gravitational lensing. Our Monte Carlo simulations demonstrate that the derived value of the Hubble constant is very sensitive to the offset between the center of the emission and the center of the variable emitting region. Thus, we propose using the value of H0 known from other techniques to spatially resolve the origin of the variable emission once the time delay is measured. We advocate this method particularly for gamma-ray astronomy, where the angular resolution of detectors reaches approximately 0.1 degree; lensed blazars offer the only route for identify the origin of gamma-ray flares. Large future samples of gravitationally lensed sources identified with Euclid, SKA, and LSST will enable a statistical determination of H0.
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