A 400 W supply doesn't really say what the average power consumption is. But if we assume that you are operating somewhere near 400 W total, including losses due to the inverter and battery, then this is 1200 WH. You probably won't get more than the equivalent of 6 hours of direct sunlight per day, which means that you would need about 200 watts of solar panels. This would not account for variations in sunlight, which could significantly reduce the stored energy. But you may not be using a full 400 W, so you may not need quite that much either.
If possible, it would be MUCH better to use a laptop versus a desktop computer if you need to run it off solar power, since the power consumption is far less.
And the lathe might add another 400 WH or so, so for that you would need at least another 70 watts of solar panels, probably more due to inefficiencies.