even if she survives mid
You have plenty of movement speed if you get Phase Boots, you've got massive range to LH from a safe distance, and even harass anybody that doesn't outrange you. You should be surviving mid, and even zoning the other mid effectively. Don't be afraid to harass with dragon slave.
not so much in the autoattack department.
What? Read her passive skill again. The attack speed buff combined with a skadi or a daedalus or some other damage item is actually very usable.
And she needs some mana items
Euls gives a decent amount of mana, and as a mid hero, a bottle helps as well. You shouldn't be getting Arcanes. Phase boots will help you rotate for ganks and to farm efficiently, as well as give decent earlier damage. Bloodstone is viable but comes on very late if you're getting euls and a blink and aghs all first. I'd only get the bloodstone in a game where aghs is unecessary... which it hasn't been.
In certain matches, even Orchid is an option and that provides some mana regeneration as well.
Start with 3 branches, null talisman, and 2 shared tangoes. Rush bottle, then brown boots. After that, go for Phase boots. Hog runes in your bottle. Depending on who you're against, you may be able to score a kill on the other mid by level 6 if they aren't careful, and you land a stun. Coordinate a gank on a side lane with heroes in that lane (because you won't have euls yet, you may need them to set up for your LSA.) Next you should be going for euls. Buy the void stone first and don't be afraid to buy it as soon as you can afford it. At this point you can rotate between lanes and jungle camps to farm. Use your Dragon Slave and LSA to farm. LSA breaks trees so use that to create more efficient paths through jungle. (like one would use quelling blade)
When you're done euls you can get a few easy ganks if they're available, especially if a teammate can help, but even solo if the enemy is out of position. Rotate between farming and kills if they're available and you should soon be able to afford your blink. Once you have the blink you can even farm in the enemy jungle without fear if you have some idea what they have warded. After blink you should be checking inventories to see if enemies are working towards BKBs. If they are, aghs is a great investment (it gives stats too and ignores magic resist - your ult's damage is effectively better after aghs even if you're not just using it to pierce spell immunity.) and if not, you could consider other items. Orchid is good if you need to silence key targets. If you build orchid, sell your bottle. Orchid + euls is enough mana regen. I've heard arguments made for Atos but I haven't tried it out yet, personally. You could grab a BKB or a Linken's sphere if things aren't going 100% smoothly and you need something defensive. This would be around the time you could go for bloodstone if you wanted to, but it honestly may not be necessary and just slows down your progression to an item that could do a lot more for you. After that stage of the game it's time to consider how you're going to wrap up the game. If you need some extra damage after blowing through your nukes and ult, or you are finding you can't catch enemies on their own, and need to be able to teamfight, an item that supplies some right click damage is viable. Blow your load of spells on one enemy, giving you stacks of your passive, and use that massive attack speed with a daedalus or an MKB or something to contribute to the fight for longer. Replacing the Phase Boots with Boots of Travel could be a good idea if you want to split push the lanes or if your team is falling behind and you can't get out to the enemy side of the map after a teamfight. While Lina doesn't have tons of tower damage, she can clear waves fast with her nukes, and the fiery soul stacks give enough attack speed to still pressure towers at least somewhat.
That was all just disorganized thoughts from someone who has mainly only played the hero in the mid lane, but try some of that, because it sounds to me like you're a bit confused about the build or execution.