[@ManyThings][@vancexentan]
I must admit I feel kind of weird about Galileo being a lancer, I can actually see Tesla being an archer, because he shoots lightning. (shh, that's totally an accurate description.) This is to quite a few people the first thing to associated with him, too. Admittedly it's a little weak, but it's an explanation at the very least.

[hider=Tesla shoots LIGHTNING]
[img]https://upload.wikimedia.org/wikipedia/commons/thumb/2/20/Nikola_Tesla%2C_with_his_equipment_Wellcome_M0014782.jpg/800px-Nikola_Tesla%2C_with_his_equipment_Wellcome_M0014782.jpg[/img]
Regardless of what may or may not be in F/GO, give this man a portable tesla cannon and he's a valid archer.
[/hider]
I could see galileo being closest to being a caster, because he may not be magical, but he was a very smart man who was known for designing and or inventing some crazy and amazing things. So with an ability to realize his blueprints and put them into existence using his noble phantasm would be interesting to me. However caster is already taken.

As a stretch with the telescope I could also see him being an archer, but again, already taken. Then there's the thing of making him a berserker, but he'd very much rely on his mind, so the mad enhancement would really make him weaker, instead of stronger.

So, it's not at all my authority to say this, but I'd rather not see Galileo as lancer. Using F/GO is silly isn't a justification for us to be nonsensical, so if it's all the same to you, as a fellow player I'd recommend actually having someone with a spear or lance to be lancer. I'm quite sure there's some smart lancers too, if you want to play a smart character. Instead if you're going for an interesting and uncommon character instead of specifically a smart one, you could do something like Berserker Tarzan or something along those lines.