The thing with the LMLM, and most pump machines, is that the three-way solenoid opens when you turn the pump off so the pressure is lost. That's why LM calls it "pre-wetting."

Might try water temp at 94C and then adjust from there. Have found that with my LM Linea Mini, water temp makes a difference.

Jeff

Have you tried asking the shop what bean and what parameters they are using?

Well, since you are in perth, no doubt the shop you are buying from has a pretty formidable filtration and remineralisation system. If they are adding carbonates back into the water, that will have an effect on making the coffee taste less acidic. You should ask them what their remineralised water specs are. If they have a tee on their water system, they may even be able to sell you some water if you bring along a big container. Otherwise, mix up or buy some mineral solutions. You can make a KHCO3 solution and add drips directly to your espresso to try to mitigate the acidity somewhat.

There are some good comments above, so apologies if I'm repeating anything below ...

As for your other comments, you seem to have wildly different burrs and espresso machine from them, and you seem to insist that you don't believe that they make a difference. Well if they don't make a difference, why didn't you and the cafe both buy cheaper equipment?

The LMLM is reputed to be pretty high quality, but it's certainly extremely feature light for the price point. One thing that you could check is if it has the 0.6mm gicleur installed for slower pressure buildup, and if it doesn't, you might want to get that and try it. Like Craig said, the problem is that if you stop the pump it will open the 3 way and cause a pressure loss. You might be able to do a hack where you grind a bit finer, start a shot, stop it just before first drops and let it sit so that the puck saturates, wait 30s, then start a shot as normal. This won't give you a low-bodied shot like in the cafe, but it might round out some of the edges and make the shot a bit more generic. The whole point of the LMLM, though, was that they made it a long time after the more feature rich GS3 and they advertised the simplicity (i.e. lack of features) as a selling point. That's why the PID doesn't even have a display on the front of the machine.

You could also have a PID offset calibration problem, or the coffee might simply require very different temperatures. Maybe try a dramatic temperature decrease. Like 82C. And also try increased temp. Like 98C. It's worth turning over all of the rocks.

Finally, I also have difficulty keeping straight the minefield world of Option-O's naming of SSP's burrs, but if these are higher extraction burrs and you are dealing with a darker roast, then you may benefit from lowering the extraction. Grind coarser, dose up higher and maybe cut your extraction a little shorter and see if that helps.

It's kind of difficult to help without knowing what the coffee is and what the roast levels are.

Before you go modding or trading in your very expensive gear, why don't you ask that cafe all the particulars? Their quantity/weight of beans per shot, their shot start temperature, shot pressure, pre-infusion times and conditions if applicable, etc. Then watch carefully as they pull a few shots, perhaps with a stopwatch (phone app of course) in your hand.

As you are a customer purchasing their beans, they have a vested interest in helping you succeed in brewing those beans into good espresso.

I think the water might be the culprit.
Try having a sample (a litre or so) of their water and to use that at home.

"Mineral water" is too vague, your "mineral water" might be very different from their water.

Remember, coffee is mostly water

Among the many valuable contributions here, what stands out most to me is what two others suggested - ask the café. Primarily get their dose and yield. Temp if available. Use their expected time as a guide for how coarse or fine to grind, but don't get hung up on nailing time exactly.

The LMLM offers limited pre-wetting control which should help your shot. Turning things on and off, however, can disturb the puck and become frustrating and hard to repeat.

Rather than pushing limits with a 19-21g dose, try 16-18 and grind fine enough to get a longer, slower shot. Practice good puck prep and do a headspace coin test to minimize channeling.

Thanks again all for the reply's.
An update for those interested.
I have had a few more chats with the baristas at the cafe (as suggested where as well) and learned a few interesting things.
Water - they run a reverse osmosis (RO) filtration system. They did offer to provide me some water to test at home, but I declined this time around as I didn't have a container.
The slayer machine is in fact a 3 group, not 4 as I originally stated, and was later corrected.
They run a 2 second pre infusion and 5 second wet/pause
Temperature 93 degrees C
21g in 42g out in ~30 seconds.
They were not able to tell me what pressure the machine was set to for some reason.

So, I ran a few more experiments at home, based on the feedback from the cafe and also your helpful suggestions.
Grinder - burr alignment was slightly off, so had a go at placing a few shims to improve alignment. Had some success there.
Water - have started using Fiji bottled water which has a higher alkalinity.
Basket - purchased a VSD 22g basket
Tamper - got myself a Pullman big step
Machine - tried running the 'plumbed in' preinfusion setting on the LMLM for 7 seconds, of which I'm not sure what pressure it actually operates at without water line actually connected.

I'm still assessing results in the cup, but so far shots have been a significant improvement. Nice mouth feel and I can taste the same fruity flavours hiding in the cup, however there still seems to be a slight astringency taste masking to which I am trying to work out if it's a balance issue, ie whether I need to hold the shot for a bit longer.

Next steps I intend to try
- RO water from the cafe.

The quest continues....

Btw the coffee is a medium roast Colombian.

OP: I've seen all the replies asking you to ask the cafe two details, dose and yield. But no one has asked the more important question. How long has the roast rested?

Buy a bag, leave it sealed and placed in a dark cool spot and let it rest 2 weeks from the roast date, maybe even 3 and try then.