Hi,
I'm planning to travel to Sydney, Australia (syd) this June. I'll probably be flying Abe-Dtw-Lax-Syd. I almost always have about 6+ hours of a layover in LAX and I do not ever leave the airport.

I will most likely be flying Delta. In the past I simply used my Amex Gold Delta card and paid the $39 lounge fee.
Since it's no longer possible to do that I'm at a bit of a loss how to get into a lounge. I will most likely be flying Economy Comfort+ and I have no status with anyone or credit cards beyond the Delta Amex.
Is it possible to buy day lounge passes to a lounge anymore? I don't care if its a delta lounge or a different one, although one with a shower would be preferable after that much travel.
While I'm willing to spend on a day pass I don't want to spend $500+ for a year pass.

What research have you done?
What has happened to the $39 lounge? DL?
Looked at Priority pass? https://www.prioritypass.com/en/loun...es-ca-lax-intl
https://www.flylax.com/
https://www.flylax.com/search-result?search=lounge
https://upgradedpoints.com/travel/ai...rport-lounges/
https://thepointsguy.com/guide/lax-l...geles-airport/

Look here-->https://www.flyertalk.com/forum/airp...?daysprune=100

You can no longer buy day passes for delta lounges or I'd be doing that.
Priority Pass is basically useless in LAX.
I've searched FT (and google, fwiw) and looked in that forum, but there's really nothing helpful that I found, certainly nothing recent. I did see I could maybe buy access to the Star Alliance lounge, but I'm not sure on that. I was hoping asking on here would generate new or better options.

Take a look at the following thread in the Los Angeles Forum:Due to the pandemic, I am not sure how up to date the information is.

If you are creditworthy and can charge $6,000 within the first six months, consider applying for the Amex Platinum card (NOT the Delta Platinum Amex card). The sign-up bonus is at least 100,000 Membership Rewards points (and maybe more if you get a targeted offer at cardmatch.com), which more than offsets the $695 annual fee. The card gives you access to Delta and Priority Pass lounges, and Amex Centurion lounges, too. (The LAX Centurion lounge is currently closed, but you'd probably prefer to use the DL lounge so that you don't have to leave the DL terminal.)

After one year, close the Platinum card, unless you think that you can get enough value from the card to justify the $695 renewal fee.

Or... for significantly less money, see if you can upgrade to the Delta Platinum AmEx. The annual fee is $225, but it gets you back to the $39 Sky Club pass, and it comes with a difficult-but-not-impossible-to-use companion pass and some fairly decent bonus miles opportunities.

And you can still cancel before renewal if it's not working out for you, or call in to downgrade back to the Gold.

If you go to:

https://www.delta.com/us/en/delta-sky-club/locations

and don't check anything about how you'd be accessing the lounge, you'll see that they have a couple lounges at LAX T2.

But if you check Delta Sky Club Single Visit Pass as your means of access, the Los Angeles lounges all disappear, so it appears that you cannot use Single Visit Passes at those locations (even though you can at some other domestic airports). This is presumably because the LAX lounges get full enough with those people who have access for other reasons.

There are plenty of other cases where lounges have limited access due to space. In many other cases, you don't find out that lounge has limited access until you arrive there and there's a sign saying that whatever method of access you planned to use is temporarily not accepted.

So at least with these Delta Gold lounges you know ahead of time you won't have access. Wouldn't it be even worse if you only found when you arrive that you won't have access?

Unfortunately, the air travel world is not set up for people getting access to lounges only here and there. It's primarily set up for either people with lounge memberships, or people flying in premium cabins internationally, or people getting lounge access due to high elite status, or people getting lounge access through "premium" credit cards.

And LAX being divided into multiple separate terminals with separate airside spaces, LAX limits your independent lounge options compared to some airports which have one giant terminal with a single airside space. If you have 6+ hours, you may want to look into what airside inter-terminal connections there are (tunnels, buses, etc) and then once you figure out what other terminals you can connect to airside you can look into all of the independent lounges in those terminals. But obviously, that'll take a lot of research.