Based on the block of code that you say you cannot modify, it looks like App Designer thinks you have manually specified all those values. Once you have manually told App Designer to use a specific value for a property, App Designer will stop automatically calculating the value for you.
In this case, it looks like XLim and YLim (and many other properties) have been manually specified to be [0 1], which means that even if you plot data spanning from 10-100, MATLAB will try to honor your request to keep the limits at [0 1], and you won't see any of your data.
This could happen if you were browsing through the list of properties and click on each one individually, and App Designer (perhaps by mistake) interpreted that as as an intent to set a value. When you set a value, the corresponding mode value toggles to from 'auto' to 'manual'. To fix it, you can toggle the mode back to to 'auto'.
For example, looking at the list, App Designer thinks that you have manually set the values for XLim, YLim and ZLim. To tell App Designer to automatically calculate those values, you need to make sure that XLimMode, YLimMode, and ZLimMode are all set to 'auto'. You can do that for the Mode property corresponding to each of the properties in the list above.
Alternatively, you can delete the UIAxes and create a new one with new default settings. You can save yourself a little time by copying the Position before you delete the old UIAxes, create a new UIAxes, then paste the old value of Position to put your new UIAxes back into the same location as the old one.
Finally, it is worth pointing out a difference between how UIAxes and Axes behave when plotting:
Regular Axes will automatically reset all the properties (including XLim, YLim, etc.) when you call commands like plot.
UIAxes will typically not automatically reset any properties when you call plot. This means that any properties you have manually specified when designing your app will be preserved after a call to plot.
This difference in behavior is based around the value of the NextPlot property. On regular Axes the default value of NextPlot is 'replace'. On UIAxes the default value is 'replacechildren'.
You can read about the NextPlot property on the documentation page for the newplot command. Commands like plot call newplot internally.
If you want UIAxes to behave more like regular Axes, you can manually set the NextPlot property to 'replace' before you plot:
app.UIAxes.NextPlot = 'replace';
or you can manually reset the axes using the cla command: