I think there's a great deal of confusion of terms here.
In order for Logistics Pipes to be able to see what's in an ME system and to pull from the ME system, there must be a Provider Pipe attached to an unconfigured ME Interface. In order for AE to see and pull from an LP network, there must be a Request Pipe attached to an ME Interface. In order for the two networks to share power, there must be a Basic Logistics Pipe connected to the ME Interface.
Also note that even if you've got Provider and Request pipes for two-way communication, autocrafting doesn't bridge the gap very well. I do not remember which network can invoke automatic crafting of items in the other, if either, but I'm pretty sure it's not both.
If you're using Logistics Pipes for automation and autocrafting and AE for storage alone, then you won't need the Request Pipe on your Interface at all. Just the Provider pipe and a basic pipe set to default route should do what you need it to do.
However, in order to actually get to your items, you'll need to have Request Pipes elsewhere in your network. These serve the same purpose as ME Terminals, and can be interacted with using a wrench. It may or may not need to be the original stone and iron Buildcraft wrench. If you place these request pipes adjacent to chests or other blocks with inventories (such as the snazzy logistics request tables), they will place requested items into those inventories; if not, the items will be spat out into open air.
Alternatively, if you just want to use Logistics Pipes to allow access to your items from anywhere out in the field, you won't need any Request Pipes at all. Just place down an enderchest next to a Remote Orderer pipe next to a Provider pipe next to an ME Interface, supply power, link your Remote Orderer tool to the corresponding pipe (however that's done), and get an enderpouch linked to the enderchest. Clicking the remote orderer on air will open an interface similar to the Request Pipe; and when you request items, they will be pulled form your ME system into the tiny little LP network, and from there pushed into then enderchest, from which you can access them via your enderpouch. Do note that you will probably not be able to access any ME autocrafting this way- if you want to have an infinite supply of torches while you're mining, for instance, you'll have to either set up the crafting of torches with LP, or set up something in your ME network to continually keep a bunch of torches stocked.
If your goal is to connect two distant ME systems together using enderchests and logistics pipes because you're too cheap for a Quantum Ring, you'll need to have a small LP network on both sides, consisting of a Provider pipe, a Request pipe, and an Inventory System Connector pipe, and a source of power. The Provider and Request pipes both need to be attached to an ME Interface, while the connector pipe needs to be attached to an enderchest. Link the connector pipes together (however the heck that's done... I know it involves creating a pair of some kind of ID card in the soldering table and then inserting one card into each connector pipe), and it should just work. Do note that autocrafting requests will almost certainly not be able to go through the bridge- each ME network (and they will need to be separate networks) will only be able to see and retrieve what is actually stored in the other. If you want to use a terminal in one dimension to autocraft stuff in your base in another dimension, use a quantum bridge.