As title, if I spend a TL to perform an attack with Vessery, do I gain the TL back from his ability?

No, because of the timing.

If you're using a missile that requires you to spend the TL to attack, you've already spent the target lock before you make your attack roll, so the target does not have a red target lock at the point immediately after your roll, so Vessery's ability does not activate.

If you're using your primary weapon, or a secondary cannon (or missile that doesn't require you to spend the TL to fire), you have not yet modified your roll with your target lock, you cannot gain a second TL as you cannot carry more than one TL on a Defender.

(edit: to clarify, I was working on the presumption that the only TL on the target is one from Vessery himself)

Actually, it's not so much a matter of timing, more a matter of what else is in play at the time of the attack.

Col Vessery: When attacking, immediately after you roll attack dice, you may acquire a target lock on the defender if it already has a red target lock token.

Vessery is designed to work in conjunction with another ship. The other ship target locks, and that opens up Vessery for his ability. Vessery can start his attack with or without a target lock on his target. If he has one and uses it to launch a missile, as long as there is still another friendly TL on the target (which would no longer be his), he gets a new TL on the defender, that he can use in the modify step.

As Slugrage stated above, if Vessery has the only TL and uses it to launch a missile, then his ability doesn't kick in, as there's no longer a red TL token on the target.

From the FAQ:

If a friendly ship has a target lock on an enemy ship and Colonel Vessery spends his own target lock to attack that ship (for example, he spends his target lock to fire a Concussion Missile), he may immediately acquire a new target lock on that ship and spend it to reroll his attack dice.

Conclusion: Always use him with a friend that can TL.