I re-ran it as a DC sweep, keeping I1 sufficiently positive.
I get pretty good agreement with the datasheet's plot, noting the polarity inversion of your circuit, up to about 4 or 5 mA.? At that point, the core log circuit runs out of steam and clips.? That is higher than the specified input dynamic range (3.5mA max), so I think it is good -- even though the ratio I1/Iref is not as high as it is shown on the datasheet plot.? Obviously, they used a smaller value for Iref in that part of the datasheet plot.
This is the first time I simulated (or even used) a log amp so I'm not an expert.