Basic reference to build from
The wallet provided in LCT is a basic reference implementation to build from as a starting place, not intended for production use without modification. Master key encryption and authorization header requirements for the API would be the recommended minimum improvements.
ElectrumSV is the trusted desktop wallet which will implement SPV as of v1.4. If you're just looking for something to run rather than building SPV into your own stack, that's the way to go.
It connects to the Block Headers Client to get any headers referenced in transactions it receives for verification. Once all checks validate, transactions are sent via Mapi to all miners.
The Wallet is the core component of the LiteClient