Wasn't expecting to be mentioned
But yes, officially you can only flirt with two at a time up until ACT 2 and then you can only fully dedicate yourself to one since you'll be forced to choose.
Keep in mind that since release there have been numerous patches that have been fleshing out and solidifying romances while also covering up numerous cracks in their walls. Not all fixes are also fully retroactive in existing playthroughs due to numerous and extensive changes, so it's not surprising that you're able to flirt with all three simultaneously in your old playthrough. There were numerous issues with romances back when the game released, for example I was able to uncover Shadowheart's secret and trigger her romantic night before even leaving the intro beach. Talk about a fast hookup
So in short, romances have been drastically fleshed out since then and you can officially only flirt with two. Once you fully dedicate yourself to one in ACT 2, the other will try to break things off. For example because you mentioned Lae'zel and Karlach, if you become Lae'zel's
zhak vo'n'ash duj, Karlach will try to break up with you. Same with any other.
Like Shadowheart yesterday auto-broke up with me in an instant as soon as I called Minthara my lover, didn't even give me a chance to speak 
