I can provide a short answer as I am in the middle of installing rear brakes. I have a 2003 E350 with an auxiliary AGM battery installed. I added a second AGM auxiliary batter in parallel charged via a CTEK DS 250. It's a fancy name for a DC to DC charger. I owned the CTEK before I owned this van. You could charge lithium via the alternator but you need a special DC to DC converter. Big $$. Lithium batteries are expensive.

The auxiliary battery is useless unless you know how to tap into it. I ran a wire from the positive to another battery. I used the vehicle frame as ground. I built my own battery box inside the van with 12-volt power plugs and USB outlets. I used an SO connector that making removing the battery simple.

Here's my workaround and my reason for charing the Lithium via solar only. We like to park and camp at places longer than 2 or 3 days. I already owned solar panels. A parked vehicle does not charge batteries. I bought a nice 138 ah Lithium iron battery and connected it to a solar charge controller that does AGM, Li, and standard lead-acid batteries. It runs independently from the house and starting batteries.

I can park almost indefinitely if I have enough sun to charge the lithium battery. At the same time, while driving, I have 2 AGM charging! These are great

If you want the simplest solution, buy a Renogy DC 50 charge controller. It charges from both starting battery and solar. I cannot use this as I run 2 solar panels in series creating more than the maximum 25 volts.

As JWA mentioned, you may want to start a new thread.

 

Don't forget to look at Redarc DC to DC Chargers BEFORE you buy the Renogy.
Has charge profiles for lithium, AGM, GEL, standard lead acid and calcium. (4 selections IIRC). It's WELL BUILT in Australia. Not China! And if you don't mind staying up late at night, You can call & talk to some real friendly Mates down under that will tell you anything you want to know about hooking it up or how things work. Yeah, They actually answer the phone! No automated Robot phone tree.
Check their web site & I think you will be impressed with their products & the R&D that goes into them. I got the (BCDC1225D) hooked up to a 110AH Deep Cycle House Battery in the back of my van to power roof vent, water pump, & a few other items. 2 years now & works as described. No Issues. Yep,It's about $100 more than the Renolgy,
And when I get around to getting a solar panel I have a charger ready to accept the input with no hassles.

 

I have heard great things about the Redarc DC to DC charger. My 2 house batteries are separated by the Ford auxiliary battery relay and the CTEK D250S. The Redarc and Renogy do not have digital input/output displays which you need. I am using a 30 A Renogy MPPT charge controller with a digital input/output display. I like the idea of one unit charging from the alternator and/or solar panels.

 

I thought the Redarc did offer some display unit? Or maybe they (recommended) me to some other product.
I don't think you "NEED" any digital display. It's certainly a nice thing to have. I guess it would have made things a bit easier for the Apollo 13 boys!
I wish I had money to spare because I would like to have a hands on look at that Renolgy unit mentioned above. In reading the specifications it does seem to do ALL the same stuff as the Redarc And maybe even a bit more considering it comes with a Battery temperature sensor.
But then I wonder just how much advantage is gained with such a device? Remember , there's a LOT of "Marketing" going on when manufactures are trying to tell you why There unit is better than someone else's.
Hey Renology, Feel free to contact me to send me one of your Chargers for (testing) so I can RAVE about it all over the internet!!!!!!

 

Both are good choices. Call each company and speak with the engineers.

 

No need to do that coolfeet, I already made my choice with the Redarc! Been happy with it now for a few years. I have put off solar panels for way to long. Can;t seem to make up my mind on what type (or what type and how to mount). Rigid units would require acquiring ladder racks & some design to attach to them. And I have to imagine at highway speeds there needs to be some serious considerations to the design so it does not end up in someones front windshield or smashed all over the highway. Otherwise it's the more costly flexible (and very thin) type.
I guess they could be glued down in some fashion. But as I understand it there are design considerations there as well. Excessive heat build up is what I think is one of the most important considerations. But I have to imaging a properly installed set glued down with (look) a heck of a lot better (and more stealthy) than units mounted to ladder racks. And portable unit's just don't do it for me. I want my solar active whenever the sun is out. Not just when I am there to (set up) portable units. That's how I see it.

 

There are diodes in the fuse box under the hood. They're shaped just like thebfuses in that panel, but they're marked with the symbol for diode on the top. It's just a guess, but if you flip the diode so it allows the electricity to flow backward, the auxiliary battery, seems to me, would feed the main battery under the hood.
I wouldn't try to crank the van with the diodes in this position because I'm not sure those little diodes could handle the current. But you should be able to charge up the battery under the hood for a few minutes, then flip the diodes again and let er rip.