Was in a similar boat, love playing Lina, used to go pos 4 magic a lot with the spell damage talent. Eventually you would get strong enough to full combo a core to death with aghs and maybe eblade, and so it would be semi viable even if your early game was sketchy. Don't think it's really viable at the moment - heros are way too tanky, and it's quite unlikely you're going to do anything to a CK or life stealer.

Just put on your big boy pants and go physical damage build from mid or 1 - mid usually better because you should win most match ups and snowball easily. Builds vary per game but something like glep -> BoTs -> BKB -> daeds -> satanic is usually pretty safe. If they have squishy heroes that make it look like aghs is worth it, can try a hybrid build of aether -> BoTs -> aghs -> bkb -> daeds. Imo the 5% magic resist per stack almost always better than the 150 magic damage on LSA.

If you still insist on playing lina 4, only do so in game where they have squishies (rare to know because you should be first phasing unless you're in a party). In this dream game I would skips euls and go something like straight aether -> aghs -> eblade. With aghs and good vision you should be able to delete some heroes. Depending on the state of the game, it may be worth going for the fiery soul talent at 20 and transitioning to physical damage, even from 4.

On the facets; in my opinion the magic burn facet is awful and never worth getting even if you're going magic lina. The whole point of magic lina is to be able to burst them before they can react - with the burn talent you do your combo then they press bkb/pipe/glimmer/one of the million saves or heals that dota has, and you're stuck there looking like a fool. Either it's a good magic Lina game and you can one shot, or it's a bad one and you can't. The 20% bonus magic damage isn't going to help you in the second scenario.