The angle you are asking about is called the Lead Angle. Lathe tools, at least the HSS ones, are ground with a geometry intended for use with the shank perpendicular to the work piece. This is why roughing, finishing and facing tools all have varying shapes and angles - the lead angle of the tool changes with its intended purpose.
The ground-in angle of the side cutting edge becomes more acute as we go from a roughing tool to a finishing tool. As this side cutting or lead angle increases, more of the side cutting edge is engaged with the work so cutting forces increase; this is why we typically will take a smaller depth of cut when finishing.
When using most general purpose lathe tools we can vary the lead angle of the tool (make the side cutting edge more or less acute) to suit our purposes by turning the lathe tool to different angles. In general, we want to use as much lead angle as the cut will allow (to produce the best finish possible) as long as there is no chatter. If we do encounter chatter, and this is most evident on thinner work pieces that deflect away from the tool, then we need to reduce the lead angle. Reducing lead angle is equivalent to reducing depth of cut and increasing feed and chatter is reduced. The reason this works is simple. As the lead angle decreases the amount of side cutting edge in contact with the work decreases so cutting forces decrease and less deflection occurs.
This is a long-winded way of saying that the angle of your lathe tool can, and should, be varied to suit your purposes. When taking heavy cuts you want to reduce the lead angle. When taking sizing or finishing cuts you want to increase the lead angle. A lot depends on how your lathe tool is shaped but, in general, these tactics will apply. Lead angle is a very useful way to modify the impact of cutting forces. Give it a try.