I think the only reason lithium comes up in relation to this is because it's lighter ... a prime consideration for Apollo missions ...they used LiOH
So sodium hydroxide is your best bet , easily obtainable and cheap , from hard wear stores in the form of beads about 4mm diam ...of sometimes flakes ...
If I were doing this I would make a vertical transparent colomb , perhaps out of plastic water bottles , fill it up with the hydroxide pellets , and feed air in through the bottom , so it passed up the colomb in between the space between the pellets , coming out the top where it should have a greatly reduced C02 and H2O content ...
Over time the pellets will get wet , the solution dripping down through the colomb , you will have to catch this some how ...it's very nasty and caustic !!
After a while you will have a lot of solution , you have to get the air incontact with this to remove the CO2 to make full use of the hydroxide
2NaOH + CO2 = ............
A much less messy alternative could be carbon , it will be bulkier , a big drum full of C with air in one end and out the other , any charcoal should work, barbecue charcoal ... and when it's full of CO2 you can easily regenerate it driving off the CO2 with fresh air
see here ...
https://en.wikipedia.org/wiki/Carbon_dioxide_scrubber