R, 34 bytes

\(x)grepl("\\bIll([^aiou]|$)",x,T)

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grepl(
  "            
  \\b          # a word boundary
  Ill          # followed by "Ill"
  ([^aiou]|$)  # followed by either a non-aiou character OR end of string"
  "  
  x,           
  T            # ignore.case = TRUE
)

Obviously we could port the same pattern used in JS answers:

R, 35 bytes

\(x)grepl("\\bIll(?![aiou])",x,T,T)

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