Surface acoustic waves are a powerful tool for controlling quantum systems, including quantum dots (QDs), where the oscillating strain field can modulate the emission wavelengths. We integrate InAsP/InP nanowire QDs onto a thin-film lithium niobate platform and embed them within Si₃N₄-loaded waveguides. We achieve a 0.70 nm peak-to-peak wavelength modulation at 13 dBm using a single focused interdigital transducer (FIDT) operating at 400 MHz, and we double this amplitude to 1.4 nm by using two FIDTs as an acoustic cavity. Additionally, we independently modulate two QDs with an initial wavelength difference of 0.5 nm, both integrated on the same chip. We show that their modulated emissions overlap, demonstrating the potential to bring them to a common emission wavelength after spectral filtering. This local strain-tuning represents a significant step toward generating indistinguishable single photons from remote emitters heterogeneously integrated on a single chip, advancing on-chip quantum information processing with multiple QDs.