The turn lanes are not displayed here. http://www.openstreetmap.org/browse/way/196834079 Probably because the right turn is using a bypass and is not at the same place where the left turn is. Not sure you know already....Bypasses are quite common.
This is an example where you have "turn:lanes = left|through;slight_right|slight_right", i.e. 3 directions "left", "through" and "slight_right", but the node 702202811 has only 2 outputs. So matching fails.
This require extra micro routing (not implemented yet) during data conversion, which would connect this info with following junction nodes.
*link does not help always, especially in urban areas. tertiary_link sounds strange and residential_link even more. Anyway, there are some characteristics for bypasses. (*_)left and/or through destinations remain the same on the following through-road segment but (slight_)right destinations disappear. Similar are lanes. The following through-road segment should not have a (slight_)right turn but else the same turns like left and through. The following turn on through-road segment and (slight_)right road segment should be within a limited range...maybe 40m. This would solve a lot of bypasses in urban areas. But it might be worth to think about how it can be marked that turn/way-intersections belong together. Maybe by a junction area