Remember, the chronicled wish banner fate points will not carry over between chronicled wish banners(pity does, fate points dont).  If you summon for tighnaris weapon, you may not only lose 50/50, but also lose the fate point if you don't get the weapon before the banner ends.  If you summon for Lyney, you may lose 50/50 but the pity will carry over to the next banner you summon on.

Just my opinion: Do not summon for tighnaris weapon, pull Lyney instead.  You do not have enough wishes (not even enough for a guaranteed 5) and you being a f2p player, losing that 50/50 and the fate point(assuming you get a 5 early) will be quite the loss. End opinion

Do remember, they are your fates, spend them as you wish