That's a pretty reasonable approach, though I believe it's possible to run those lights directly from batteries if you make up the right cables.
Total load is 540 watts, so a large 12V, 220Ah leisure battery will in theory give you four hours. However, that's a load of 45A, which is quite high, and you will get much less than that in practice. It's better to use several batteries in series to create a higher voltage, say four for 48V, and using an inverter designed for 48V input. This distributes the load and reduces current to 10-12A, which is much kinder to all the electronics and will produce a more efficient setup.
There are significant safety concerns with all this. Wear eye protection and heavy gloves when making connections, and ensure everything is isolated properly for transport and while rigging. High power, low voltage systems like this will react energetically to being shorted out. Use heavy cable, as 12A is not a small load.
Your battery purchase should include good quality chargers. Lead acid batteries are a primitive and ancient technology but they are very difficult to charge well, and may explode (venting boiling acid and lead shrapnel) if mistreated. Charging them will tend to take more hours than there are between wrap and call, so if you need to do multiple days in a row, you may need more than one set.
Hope that helps.