There is no change in this interaction. As for whether it deals 8 or 10, that's a decision made by the player taking the damage (they'll likely choose only 8). When multiple replacement effects attempt to replace the same event, the affected player (guy taking the damage here) or controller of the affected object(s) chooses which to apply first, and then if the other is still applicable to the now replaced event, they will still be applied afterward.
With Lightning Bolt, Pyromancer's Swath, and Furnace of Rath (Please include oracle texts in the future)...

|Instant| Lightning Bolt deals 3 damage to target creature or player.


|Enchantment| If an instant or sorcery source you control would deal damage to a creature or player, it deals that much damage plus 2 to that creature or player instead. / At end of turn, discard your hand.
... Lightning Bolt's effect deals 3 damage. Both Furnace and Swath attempt ot replace this event. The player taking damage may choose which to apply first. If he applies Swath First, the event is now "5 damage," which Furnace then replaces with "10 damage." If he applies Furnace first, the event becomes "6 damage," which Swath replaces with "8 damage."
419.9a. If two or more replacement or prevention effects are attempting to modify the way an event affects an object or player, the affected object's controller (or its owner if it has no controller) or the affected player chooses one to apply. Then the other effect applies if it is still appropriate. If one or more of the applicable replacement effects is a self-replacement effect (see rule 419.6d), that effect is applied before any other replacement effects. If two or more players have to make these choices at the same time, choices are made in APNAP order (see rule 103.4).