From Safelinks Terms and Conditions....
You may be able to activate the Service on a compatible, unlocked handset You provide Yourself (Bring Your Own Phone or BYOP). Some SafeLink features are available only on SafeLink handsets and will not be available with BYOP. If you are activating your Service with BYOP, you must use a compatible phone that does not interfere with our Service and complies with all applicable laws, rules and regulations.
Devices capable only of using data are strictly prohibited and Your use of any such device is grounds for immediate termination of Service without a refund. You are responsible for ensuring that your BYOP wireless phone is compatible with the Service and meets all Federal laws and standards. You are further responsible for the purchase and maintenance of any additional hardware, software and/or internet access required in order to use the Service.
SafeLink Service will only work with wireless devices that are compatible with our network. Not all services are available with all wireless devices or on all networks. We may remotely change your wireless phone’s software, applications or programming without notice. This could affect your stored data, your phone’s programming and how you are able to use your wireless phone.
So that would be a no, since your LG phone uses data. Although I do know that in California the laws are different. So If you live there, I would definitely call Safelink directly. Otherwise you are out of luck.