Is this V10?
For background information, is this a duplicated copy of the original model or a re-use for the new report because the old report is not longer used?
Do the lookup (I assume internal from reading the problem) values conflict between the reports of could all values co-exist shoul dtha be desirable?
Does "Get Input values" append the values found in the new report to the old values? Could you delete the existing entries and then update the values?
In what way would deleting and recreating the field affect other calculated fields? In theory any calculated field relying on the lookup field should continue to work once the field exists again. However if the working of the calculation relies on the value returned in the field from the lookup you may have problems where lookup results are different - but of course you may have problems anyway if the values are different.
If these lookups are consistent (but different) per report you could consider creating your own reference model of useful fields (and fuinctions and whatever else) and keeping each lookup set in there with unique identifying names.
Your operational models (you would need 2 versions in this example) could then link the lookup field to the appropriate field from your User Defined source model. That way you have one main report model to maintain with a minor adjustment for one field between the 2 (or more) versions. However as described here I'm not sure you really need to go down that route. Separate models with their own internal lookup tables should work well enough.