The question could he take 2 weapon fighting to reduce that penalty?
No, the TWF feat only reduces the penalties for usign the two-weapon fighting rule option (on CRB pg. 202). Natural attacks are completely seperate from that (and indeed, nothing that references main-hand or off-hand affects natural weapons). The only thing that directly reduces the penalty for secondary natural attacks is the Multiattack feat, but it requires three or more natural weapons.
And would it make a difference if he made Kobold or Ratling tail weaponry for his tail and size?
Both Kobold Tail Attachments and the Ratfolk's Tailblade keep the tail as a natural weapon, so no, it wouldn't change anything (except make enchanting it cheaper).
If something would make the tail use the manufactured weapon rules, this FAQ would make it unusuable alongside a two-handed weapon.
Usually, combining natural and manufactured weapons is not worth it if you need to put investment into it. In additional to the -5 penalty to attack rolls and only half strength bonus to damage rolls the natural attack suffers, you natural weapon would take additional gold to enchant (or lack the benefits of an enchantment, more likely), and if you have any feats like Weapon Focus for your main weapon, won't benefit from those. It's usually not worth to spend a feat, as higher and higher weapon enchantments become the expectation, and DR becomes more common and higher in amount.
A lizardfolk character (from the Advanced Race Guide race builder examples) already has a bite and two claws and should be able to take Multiattack.
To qualify for Multiattack with another character, a two level dip in ranger (or slayer) will allow the character to take the Natural Weapon Combat Style feat Aspect of the Beast (Claws of the Beast) to gain two claw attacks. As long as the character already has one natural attack (such as half-orc with the Toothy alternate racial trait), that gets them to the "three or more" threshold.
If you time the second level of ranger (or slayer) for an odd character level, you can take the Multiattack feat at the same time as Aspect of the Beast.
To qualify for Multiattack with another character, a two level dip in ranger (or slayer) will allow the character to take the Natural Weapon Combat Style feat Aspect of the Beast (Claws of the Beast) to gain two claw attacks. As long as the character already has one natural attack (such as half-orc with the Toothy alternate racial trait), that gets them to the "three or more" threshold.
I really hope this was more brainstorming than an actual suggestion...
I don't want to be mean here, but seriously, spending two levels and a feat just to make the crappy bite you're adding to your weapon attack slightly less bad is not the way to improve your character. Even if you qualify for it without further investment, for a single natural weapon, Multiattack is not worth the feat.
If anything, this should be a one-level dip into Shifter, using the Alternate Natural Attacks option from Ultimate Wilderness to get two talons or such, so that the character could ad least actually use all three natural weapons alongside their manufactured weapon.
Still, I would always advice against building to combine natural and manufactured weapons. If you invest enough to make the natural attacks actually worth it, you're likely in a situation where fully focussing on them would be better.
All that said, even without multiattack a -5 penalty is not so bad. It is only the same penalty as your second iterative attack and those hit most of the time once you have a few levels under your belt.
You're forgetting that your iterative attacks* profit from your weapon's enchantment bonus, as well as feats and class features that you may have that improve your main weapon (like Weapon Focus or Weapon Training). The OP's character is a Ranger, so class features would still apply, but only in situations where the character is already at their best.
*) by the way, that term describes the additional attacks form high BAB, so the one at -5 would be the first iterative attack.
There is a feat that might work for the half strength that would be double slice.
Which part of "nothing that references main-hand or off-hand affects natural weapons" do you not understand?
"Off-hand" and "secondary" are completely seperate things. You can't just take something for one and apply it to the other. Indeed, not one of the bonus feats from the TWF combat style would do anything for natural attacks.
The bite and claws on a lizardfolk suck for damage. The tail isn't too bad.
Wait, what? A tail slap from Dangerous Tail is 1d4 base damage, how is that "not too bad" but the claws for identical damage and the bite that's behind just 0.5 average damage "suck"?