Upcoming space-based integral field spectrographs will enable spatially resolved spectroscopy of distant galaxies, including at the scale of individual star-forming regions (i.e., down to just tens of parsecs) in galaxies that have been strongly gravitationally lensed. In the meantime, there is only a very small set of lensed galaxies where such spatial detail is possible at wavelengths containing important rest-optical emission lines, even with the Hubble Space Telescope's Wide Field Camera 3 infrared channel grisms. Here, we examine two of these sources, SDSS J1723+3411 and SDSS J2340+2947, using HST WFC3/IR grism data and supporting spatially unresolved spectroscopy from several ground-based instruments to explore the size of spatial variations in observed strong emission-line ratios like O32 and R23, which are sensitive to ionization parameter and metallicity, and the Balmer decrement, which is an indicator of reddening. We find significant spatial variation in the reddening and in the reddening-corrected O32 and R23 values that correspond to spreads of a few tenths of a dex in ionization parameter and metallicity. We also find clear evidence of a negative radial gradient in star formation in SDSS J2340+2947 and tentative evidence of one in SDSS J1723+3411, though its star formation is quite asymmetric. Finally, we find that reddening can vary enough spatially to make spatially resolved reddening corrections necessary in order to characterize gradients in line ratios and the physical conditions inferred from them, necessitating the use of space-based integral field units for future work on larger, more statistically robust samples.