Key error when trying to add a new attribute value to feature - PyQGIS3

A warning in updateFeature() documentation:

This method needs to query the underlying data provider to fetch the feature with matching QgsFeature.id() on every call.

Try in this way:

v_layer.startEditing()
iterator = v_layer.getFeatures()
seg = next(iterator)
seg["FieldOne"] = "fieldone"
seg["FieldTwo"] = "fieldtwo"
v_layer.updateFeature(seg)  
v_layer.commitChanges() 

or in this way for all features:

v_layer.startEditing()
for seg in v_layer.getFeatures():
    seg["FieldOne"] = "fieldone"
    seg["FieldTwo"] = "fieldtwo"
    v_layer.updateFeature(seg)  
v_layer.commitChanges() 

EDIT: If you want to set the values ("fieldone","fieldtwo") only for the feature that you just created, you have to set fields for new QgsFeature object using setFields() method.

def createNewFeature(fieldone, fieldtwo):
    seg = QgsFeature()

    # set fields for new object
    seg.setFields(v_layer.fields())

    # set attribute values for fields
    seg['FieldOne'] = fieldone
    seg['FieldTwo'] = fieldtwo

    # set geometry. change start and end points
    seg.setGeometry(QgsGeometry.fromPolyline([QgsPoint(1, 1), QgsPoint(2, 2)]))

    # add new feature to the layer
    pr.addFeatures([seg])


v_layer = QgsVectorLayer('LineString?crs=epsg:4326', 'layerName', 'memory')
pr = v_layer.dataProvider()
pr.addAttributes([QgsField('FieldOne',  QVariant.String)])
pr.addAttributes([QgsField('FieldTwo',  QVariant.String)]) 
v_layer.updateFields()
QgsProject.instance().addMapLayers([v_layer])

createNewFeature("field one", "field two")

You can use the setAttributes function:

v_layer = QgsVectorLayer('LineString?crs=epsg:4326', 'layerName2', 'memory')
pr = v_layer.dataProvider()
pr.addAttributes([QgsField('FieldOne',  QVariant.String)])
pr.addAttributes([QgsField('FieldTwo',  QVariant.String)]) 
v_layer.updateFields()
QgsProject.instance().addMapLayers([v_layer])
seg = QgsFeature()
seg.setGeometry(QgsGeometry.fromPolyline([QgsPoint(10,10),QgsPoint(11,11)]))
seg.setAttributes(["a","b"])
pr.addFeatures([seg])

You just set the attributes with the coordinates as you create the feature.