How to deal with an offlane Darkseer early game?

Lina should be able to zone out Dark Seer. Lina has the 2nd highest attack range in the game(after Techies) and she should be standing in the woods/sideshop autoattacking the Dark Seer.

Keep in mind that Dark Seer is arguably the best offlaner atm. He's the tankiest level 1 hero after Spirit Breaker and Ogre Magi (and Medusa with mana shield).

As for Phantom Assassin, I would recommend killing the creep with the ion shell first. She could also go for last hits with dagger. Lina could go for a bottle, to keep Phantom Assassin/ herself safe.

EDIT:

As Phantom Assassin, a battlefury is a common item in general, the component called Ring of health is an amazing item in lane. People sometimes also just buy a Ring of regen vs a dark seer because of the cheap cost.

NOTE: Ring of regen, Ring of health, Void stone, Perseverance and Sage's mask are partially shareable.

From the wiki:

This means that other heroes can pick them up and benefit from the effect of the item, but cannot sell or upgrade the item.

Which means your support could just buy a ring of health and give it to you for you to use in lane.

Further note that I'm not looking for advice on counterpicking (I realize a support with two reliable stuns would help a lot here...): I want to know what to do when I end up in this situation.

Uhh... that kind of depends on the heroes you end up with. I can't predict the future so I won't know your full array of options. Ranged support and melee carry covers a very wide variety of heroes, the main decider being "does one of you have a reliable stun or silence?"

However, if you can't farm consistently in your lane as a melee carry, your objective is pretty much always the same: build enough items to farm jungle only, and then do that instead. In PA's case, probably just rush Morbid Mask and get a Stout Shield if you don't already have it. You can lifesteal off of jungle camps, which do less damage than the ion shell, then return to lane to farm a couple of waves when your life is full, then return to jungle when your health gets lower again, etc. Your Lina should be able to hold the lane by herself fine against a solo Dark Seer. This is good for Lina, because if she can use the gold she gains to buy a Eul's Scepter, then you can get kills on Dark Seer when he tries to push the lane again. He can still put ion shells on incoming creep, but you will be able to zone him out of XP range.

So, important general things:

• Get reliable disable via an item choice if you don't have it already
• Farm woods if you don't have anything that allows you to simply sustain the ion shell damage

Another thing you can do is have Lina fight elsewhere on the map, always when you have greater numbers in the fight. This will prompt their team to either lose the fight, or group up as 5, and if Dark Seer leaves his lane then PA can free farm for a few waves. This sounds like it requires coordination, but if you buy a smoke and ping it enough times in woods near their lane people will eventually get the idea.