I found this birth
Alexander FRASER
Christened 22 JUL 1817 Inverness, Inverness, Scotland
Parents Simon FRASER and Elizabeth McGREGOR
Extraced from local records
Not sure if this is the right one as i also checked for children of Simon & Lillias and found the following:
JOHN FRASER - International Genealogical Index
Gender: Male Birth: 17 APR 1823
2. JOHN FRASER - International Genealogical Index
Gender: Male Christening: 24 APR 1823 Croy And Dalcross, Inverness, Scotland
3. ANDREW FRASER - International Genealogical Index
Gender: Male Birth: 13 MAY 1826
4. ANDREW FRASER - International Genealogical Index
Gender: Male Christening: 16 MAY 1826 Croy And Dalcross, Inverness, Scotland
5. ANNE FRASER - International Genealogical Index
Gender: Female Birth: 13 MAY 1826
6. ANNE FRASER - International Genealogical Index
Gender: Female Christening: 16 MAY 1826 Croy And Dalcross, Inverness, Scotland
7. JONATHAN FRASER - International Genealogical Index
Gender: Male Birth: 09 AUG 1813
8. JONATHAN FRASER - International Genealogical Index
Gender: Male Christening: 24 AUG 1813 Croy And Dalcross, Inverness, Scotland
Could be the first one was trnascribed incorrectly perhaps.
Hope this helps you
Amanda