How can I implement a solid state relay in LTSpice?
PlasmaHH is right. The component you look for is simply the "SW", or voltage controlled switch.

However, in addition to the switch component itself, you need a directive on your schematic to define its characteristics, like that: .model MySwitch SW(Ron=1 Roff=100Meg Vt=3) (Vt is the threshold).

Finally, right-click on the SW component and set its value to "MySwitch".