Yes it is and there's a few type 1 low-carbers on this forum. You can eat a carb-free lunch but depending on what you eat and the quantity you may still need to inject some insulin, trial and error by testing your postprandial bg will soon tell you by how much.
As Noblehead says the answer is yes. Any normal healthy person can follow a low-carb diet. Set yourself a daily carb target and spread the carbs thru the day but you don't have to have them with every meal. Match your insulin to the carbs for each meal as usual
You do really need to be on the dose-adjustment regime rather than having a set amount of mixed insulin each day. Do you carb-count and adjust your fast-acting insulin accordingly? If so, then like the others said, just adjust your insulin dose according to how many carbs you eat with a bit of trial & error to get it right. I think it's probably a lot more tricky trying to low-carb on a set-dose regime unless you're low-carbing all day every day.
I did a low carb diet for 8 months although it did get a bit boring and I couldn't sustain it any longer. Lost 2 stone though!
I completely said goodbye to Novorapid which was great as I no longer feared hypos (lantus can make you hypo but it's rare compared to NR in my experience) . I dropped my lantus from 28 u to 12u per day.
Yep, I low carb. Works great for me. In all likeliness, you will still need Novorapid, mine halved. With LCing, you should lose weight as insulin is used to synthesise fat into fat cells, so if you take less insulin, you should lose weight too. In addition you should see fewer highs and less frequent and milder hypos.
I lost 2st by following the Slimming World diet, it's very good for diabetics as you can eat lots of the carbs you need and still lose weight, I even managed to half my insulin levels along the way.