This was the matchup every game like 5 years ago, and since then I've felt like lulu can get through 1-5 if you play it right and outscale at 6.

Lvl 1 go E because Karma Q outranges Lulu Q, you can't really try and trade Qs or you get spaced and take a lot of damage. Instead with E the lvl 1 makes a lot of sense. Mantra Q you can't avoid but with E you can just shield it. If Karma doesn't have mantra, you can easily contest bushes and try to shield yourself and auto her. If you dodge the normal Q you comptletely win the trade - your shield takes all her damage and your auto gives you two spellthiefs procs (spellthiefs > relic on lulu in most or all soloq games imo). Even if she hits a normal Q into your E the trade is good for you if you auto her, and it's eh fine whatever if she gets a normal Q and an auto into your E in exchange for an auto.

Ofc adc, lane state, jg, and all the stuff that goes on in a real game matters too for if you can trade or not. Also worth noting a lot of Karmas go scorch/biscuits/time warp tonic, and not that it makes a huge difference or really changes how you play situations but it does commit them to trading a bit more than you, so this lulu E approach is nice in these situations because you want to play reactively when the onus is on Karma to walk up and trade.

Lvl 2-5 you probably need 3 points in E for trades. One other thing is to bind the self E key so you can easily shield yourself if Karma Qs you, even if you start with your mouse hovering over your adc.

Post 6 you get an ult and Karma doesn't, so you do more in fights.