My DD also constrained her list to Engineering/CS with liberal arts. Had Robotics/CS/etc. in HS and wanted to ensure she had Engineering as an option. As others have posted and I'm sure you've found elsewhere, LAC with Engineering is nearly non-existent. Because the list of LAC/Engineering schools was so small, DD ended up expanding her list to include smaller universities - RPI/Leigh/CWRU/... That still ended up a fairly constrained list...
In the end, DD ended up in CS/Math - NOT Engineering. Had she started with CS/Math, there are a LOT more LAC options.
If your DD decides that it'd be OK to forego Engineering, I'd suggest starting with the NSF Doctoral feeders list...
https://www.nsf.gov/statistics/infbrief/nsf13323/
For Engineering and LAC, google "abet accredited LAC" - There are several good conversations about LACs with Engineering/3+2/Physics Major with MS Engineering & a small number of additional LACs with engineering or engineering LACs that haven't been discussed yet.