We show that an ion-ion cross-field streaming instability between cold newborn cometary ions and heated heavy ions that were picked up upstream is likely a contributing source of observed lower hybrid (LH) waves in the inner coma of comet 67P/Churyumov-Gerasimenko. Electric field oscillations in the LH frequency range are common here, and have previously been attributed mainly to the lower-hybrid drift instability (LHDI), driven by gradients associated with observed local density fluctuations. However, the observed wave activity is not confined to such gradients, nor is it always strongest there. Thus, other instabilities are likely needed as well to explain the observed wave activity. Several previous works have shown the existence of multiple populations of cometary ions in the inner coma of 67P, distinguished by differences in mass, energy and/or flow direction. We here examine two selected time intervals in October and November 2015, with substantial wave activity in the lower hybrid frequency range, where we identify two distinct cometary ion populations: a bulk population of locally produced, predominantly radially outflowing ions, and a more tenuous population picked up further upstream and accelerated back towards the comet by the solar wind electric field. These two populations exhibit strong relative drifts ($\sim$20 km/s, or about 5 times the pickup ion thermal velocity), and we perform an electrostatic dispersion analysis showing that conditions should be favorable for lower hybrid wave generation through the ion-ion cross-field instability.