Downloading lossless to my iPhone?

So I guess I’m like 1 of 8 people that spent money purchasing a Wadia iPhone digital transport on the used market( because they are out of production) thinking that I could play lossless/ cd quality music from my already purchased iTunes music, on my entry level hifi Cambridge integrated Cxa80. So after hours of reading bits and pieces of what’s possible with iOS lossless and what’s not possible, I decided to go into an Apple store to find out from the corporation directly. I had to fib on my issues when trying to make the in-house appt because when I mentioned lossless it would direct me to an email chat that has been a waste of time in the past. So I get to the shop, tell them that I need help downloading lossless music from my iTunes collection,so I can enjoy my hifi system I recently purchased, the gentleman asked me with a straight face..” what is lossless”? So a 2nd guy listened to my question, and had to go research it in the back for 5 min, only to comeback to tell me that you cannot download iTunes music in lossless... you can only convert ripped music to the apples ALAC lossless.. but cannot convert or re-download purchased albums in lossless. Well isn’t that rich. Gentleman....( there’s no ladies on a forum like this) is this true?? I really didn’t want to set up a computer to purchase hi rez albums and plug into my amp, but if this is true, then that sounds like my next option. Any suggestions on how to get lossless iTunes music on my iPhone would be great.
My gear is recently used market 3/7 Dynaudio towers, Wadia digital iPhone transport, a new cxa80 digital integrated amp, an n-30 pioneer music streamer, a low cost 12 inch Polk sub($250 range) that I dragged out of my tv room,kimber braided speaker cables, and a shuyata venom power conditioner plugged into a cheap power strip without a surge filter.
Thanks for reading.

I left iTunes many moons ago, and that is one of the reasons.  Have you considered a Tidal HiFi membership? All albums in CD quality FLAC files, streamed. You can also download if you like.
I don’t think my pioneer streamer works with tidal (or any streaming services other than internet radio,) and my phone would still not be able to hold the lossless albums right? 
You can put lossless audio files on your iPhone, and then play your iPhone through your system using the Wadia transport and an outboard DAC if you like. You won't need a computer to play those files through your system. I'm not very familiar with Apple products, so I'm not sure if you need a computer to get your files onto the iPhone. I would think there would be a way to avoid requiring that.
Agreed. Check out onkyo’s high res player app. You can use it to load high res files on the phone. But you can also try the Tidal app on the phone, played in your Wadia Dock.

please tell me more about your entire system. Where does the pioneer streamer fit in? What is the model number? Where does your music reside?
I play Redbook and Hi-Rez lossles files on my iPhone using the Onkyo player, by outputting the bits through the lightning port using the USB "camera" adapter, into a Audioquest DragonFly portable DAC, then corded Shure or UE earphones.  Not as good sounding as a Schiit MultiBit, but pretty good for the road and plane.
I am a Tidal subscriber and pay 19.95 per month for their HiFi tier.  The Tidal app on my iPhone lets me download full resolution 16/44) songs/albums/playlists to the phone for playback.  Recently upgraded my phone to 256G of memory for this purpose. Awesome.  

I usually use home WiFi to download but occasionally, when I absolutely have to hear an album right now, I will download over the LTE network.  

No streaming hiccups this way.  And I have a ton of Apple iTunes music on my home server that isnt on my phone. Easier to listen thru Tidal downloads.  
Gentlemen , thank you for your insight, I think I’m getting closer to figuring this all out!!
To marktomaras-
 my music source  is pretty much all on my iPhone, older purchased albums on iTunes and for the past year or two, albums from Apple Music that are downloaded ( I guess for as long as I keep paying for the monthly). My stereamer is a Pioneer Elite n-30 and is mainly  for ambient and smooth jazz playing for everyday listening.

ive been thinking about tidal but haven’t researched it too deeply because I was trying to accomplish hi-res with my iTunes then pipe it through the Wadia transport directly into the hifi dac in my amp, but iOS stinks.

To dbtom and everyone still interested in my hifi issues... I can download or steam hi Rez albums from tidal, better than cd quality, and run through the Onkyo or tidal app, then bypass the junk dac on the phone, into the hifi dac on my amp?!!! Or would it only be cd quality( not hi res)?

and while you are all still reading my babble... is there a sound quality improvement  to downloading an album on my iPhone from tidal vs streaming an album from tidal? 

(If if I can download ship of fools in hi res on my phone, and play it through my gear, then things are going to get pretty bitchin!)