If someone touched a cold sore then touched another lips can the person get it and how long does the virus survive on fingers if fingers not washed ?

Possible, but...: We don't worry much about lip cold sores except that we don't want to transmit it to young babies. Children naturally often catch oral herpes (cold sores) from family members. For everything about germs, check the Canadian website: https://www.canada.ca/en/public-health/services/laboratory-biosafety-biosecurity/pathogen-safety-data-sheets-risk-assessment.html