When using nodal analysis of a circuit involving CCCS, how do you know which currents are entering and which are leaving?
Your paper analysis is correct, but your LTspice simulation is incorrect. I get the same (incorrect) result as you if I use a gain of \$+29\$ for the F device (your \$I_1\$). But the gain should be \$-29\$ since \$i_b\$ flows from the negative to positive terminal of \$V_{\text{ib}}\$. Changing the gain gives you the correct result.

Circuit:



F device attributes:



Result:



If I change the gain to \$+29\$ the result is:



Note that the simulation result is \$v_y = v_{y1} - v_{y2} \approx 98\$V when using a gain of \$+29\$, which is clearly wrong.

The two simulations highlight the importance of maintaining consistency in the direction of currents. The problem statement defines \$i_b\$ and \$29i_b\$ as both flowing toward the middle "T" node. LTspice defines \$i_b\$ as flowing away from it since it defines the current through \$V_{\text{ib}}\$ as flowing from positive to negative terminal. That means you also have to define the CCCS \$29i_b\$ as flowing away from the middle "T" node. In the incorrect simulation (with gain of \$+29\$), \$29i_b\$ is still flowing toward the "T" node while \$i_b\$ is flowing away from it. The correct simulation defines them both as flowing away from the "T" node. Alternatively, you could just switch the direction of the "F" device and use a positive current gain -- it would then also be defined as flowing away from the "T" node.