A couple of points:
Normally LTSpice will attempt to calculate the steady state voltages on capacitors, which can cause problems in circuits like this, which don't have a steady state. One way round this, is to set the initial voltage on the capacitor to zero, using the Ic (Initial Condition) directive.
LTSpice already has built-in models for logic gates and Schmitt triggers. There's normally no need to use custom ones, unless one is doing something unusual, such as manipulating the supply voltage, or relying on the supply current. They're in the [Digital] of the Insert Component Symbol dialogue box. More information can be found in the LTSpice help file: Circuit Elements > A. Special Functions.
Here's an example of a Schmitt trigger oscillator, using a parameters which model the 40106. It's probably not perfect, I quickly looked at the data sheet and adjusted the model accordingly, but it should be good enough for most applications. Note the data sheet specifies the hysteresis voltage differently to LTSpice. The data sheet lists the hysteresis as the difference between the positive and negative going thresholds, where as LTSpice adds and subtracts is from a defined from the parameters, given in the help file. This means LTSpice's parameter for hysteresis should be half of that on the data sheet, hence why I've got 0.45V, rather than 0.9V for Vh.
