IR2110 Simulation not working in LTSPICE
It looks like you used an autogenerated symbol for your IGBT, but you connected it wrong, because the order of the pins is D-G-S. But, instead of using an autogenerated symbol you can make things easier for you if you choose the [Misc]/nigbt symbol, which you can use directly as an IGBT. All you have to do is rename NIGBT with STGW40H60DLFB-V2, and you're done.

You still have to add the correct prefix (right-click on the symbol, change Z to X), I thought that would be implied.
Anyway, the IGBT subcircuit is full of behavioural expressions and it's not very convergence-friendly. I don't know if it will help with your particular schematic, but I poked around and managed to get it working in a simple test by making these changes inside the STGW40H60DLFB-V2.lib file:

on line 70 change r_escusione 1z a1 500 to c_escusione 1z a1 10p Rpar=500
on line 73 change r_conv1 1y a1 10 to c_conv1 1y a1 10p Rpar=10
on line 114 there's a Grg1 ...; add this line, crg1 g2 g 10p rpar=1g right below it
on line 168 add a ; at the beginning of the line, in front of E2 ..., then add these two lines below:

g2 50 40 g d1k 1k
r2 50 40 1m


on line 204 add a ; at the beginning of the line, in front of E22 ..., and add these two lines below:

G22 502 402 ss d1k 1k
r22 502 402 1m

You can help in your schematic by setting Rser=10...100m for the voltage sources (V3, V4, and V1; V2 can be ignored), adding Rser=1...10m to capacitors (all four), and adding Rpar=10...100k to the inductor. Also try changing V2, A1 and their connections like this:

delete A1 and all the connections to the input pins HIN and LIN. V2 should be just sitting there in the schematic with no connections.
add [Digital]/buf (not buf1) and connect its input to V2 and its outputs to HIN and LIN pins. There should be a new A1 in the schematic.
add vhigh=6 tau=10n tripdt=30n to the new A1.

These changes could help, too:

add Vp=0.3 to the .model UF4007 card
add this model for the 1N4148:

.model 1N4148 D(Is=2.52n Rs=.568 N=1.752 Cjo=4p M=.4 tt=20n Iave=200m Vpk=75 Vp=0.3 mfg=OnSemi type=silicon)

Try running your schematic with these changes. If you're religious, praying might help.