At least a fraction of gravitational-wave (GW) progenitors are expected to emit an electromagnetic (EM) signal in the form of a short gamma-ray burst (sGRB). Discovering such a transient EM counterpart is challenging because the LIGO/VIRGO localization region is much larger (several hundreds of square degrees) than the field of view of X-ray, optical, and radio telescopes. The Fermi Large Area Telescope (LAT) has a wide field of view (∼2.4 sr) and detects ∼2-3 sGRBs per year above 100 MeV. It can detect them not only during the short prompt phase, but also during their long-lasting high-energy afterglow phase. If other wide-field, high-energy instruments such as Fermi-GBM, Swift-BAT, or INTEGRAL-ISGRI cannot detect or localize with enough precision an EM counterpart during the prompt phase, the LAT can potentially pinpoint it with arcmin accuracy during the afterglow phase. This routinely happens with gamma-ray bursts. Moreover, the LAT will cover the entire localization region within hours of any triggers during normal operations, allowing the γ-ray flux of any EM counterpart to be measured or constrained. We illustrate two new ad hoc methods to search for EM counterparts with the LAT and their application to the GW candidate LVT151012.