LTspice: Including Time Derivative of a Node Voltage in Initial Condition
I'm not entirely sure about your question. But I think you are having trouble specifying the initial condition for the first derivative of \$V_1\$.

If so, I don't know of a method of doing that with LTspice.

However, you are able to specify the initial conditions for any voltage node and for the current in any inductor. And that's how I'd approach this.

You know that \$V_{1_{t=0}}=2\:\text{V}\$. You also know that \$\frac{\text{d}}{\text{d}\,t}\:V_{1_{t=0}}=0\:\frac{\text{V}}{\text{s}}\$. Given this last bit, you know that the instantaneous current in \$C_1\$ must, by definition, also be zero. You can easily calculate the current in \$R_1\$, given \$V_{1_{t=0}}=2\:\text{V}\$. Therefore, you know the initial current in \$L_1\$. (You must easily see what I'm suggesting here.)

So this means you can specify this initial current in \$L_1\$ using the ".ic I(L1)=??" card. Yes? Try it out.