Sign of current through a voltage source
the current across the voltage source is shown to be negative (-.05)


Before getting into the meat of your question, we normally say that current flows "through" a device, not a "across' it.


  That means in this case they mark the current coming out of the the positive terminal of the battery as negative. Is that just a convention or is there some logic behind it?


This is the passive current convention. It is widely used (Wikipedia says "universally") in electrical engineering.

If you use this convention consistently, then when you calculate the power \$P\$ associated with the component, you will always know what the sign of \$P\$ means.
If you calculate

$$P=IV$$

with the signs defined by the passive current convention, then a positive \$P\$ means that the component is receiving power from the rest of the circuit, and a negative \$P\$ means that the component is delivering power to the rest of the circuit. Therefore when we use voltage sources to deliver power to the circuit, we expect the current through the source to have a negative sign.


  If it's a convention, is that the general standard?


This is the most common standard, in my experience, when somebody actually thinks about using a standard convention to define the current direction. 

It's also common, at least in one-off calculations, to simply do things ad hoc, and assign the sign of currents arbitrarily or according to what the engineer thinks will end up giving positive values in the solution. But that doesn't really apply to the designers of LTSpice, who had to choose a convention for any circuit a user might come up with.