(I'm writing this brief post for /u/FelidarSovereign.)
In this post, segments and repeats are different things.
Square shawls knitted in the round usually have 4 segments, but often have repeats of any number of stitches within each segment.
1. Knit in the round
Most people knit faster than they purl, particularly if they knit continental.
I find that garter lace is harder to fix, despite having been playing around with it for awhile. Many traditional garter lace patterns also have wrong-side patterning, which is troublesome for lifelines if you need them.
Knitting in the round also has the advantage that as your rows grow larger, you will not have to turn your work.
2. Minimise beading
Beading is pretty slow, unless you pre-string, but I have not worked with pre-strung before as I knit with very fine yarn, and I worry about the wear and tear on the yarn.
3. Choose your Left Leaning Decrease wisely
I use the SSK variation that Brooklyn Tweed recommends in their patterns, because it is very fast. I believe I first came across this in Permafrost by Jared Flood. Slip the first stitch as if to knit, then knit it and the next stitch together through the back loop. Naturally, if you need a 2-stitch left leaning decrease, you slip the first stitch, then knit it and the next 2 stitches together through the back loop and so forth.
If you're using yarn that is at least 1300m per 100g, I advocate just knitting or purling the stitches together through the back loop. You will not be able to tell the difference anyway.
4. Decrease in one movement
When you k2tog/k3tog/kxtog, it's about as fast as any other knit stitch.
One of the reasons why I like BT's SSK variation (see point 3 above) is that it is very easy to knit it in one movement, none of this passing stitches back and forth nonsense.
You can also do a CDD and other multi-stitch decreases in this manner. I actually find this to be easier to achieve with finer yarns.
This is important to speed because lace patterning is the result of planned decreasing and increasing, and the more intricate the lace, the more decreasing there will be.
5. Short repeats
Short repeats are faster to memorise, and require less checking back and forth with the chart/instructions.
You will likely also find that you will be much faster at finding mistakes when you need to.
6. Use fewer stitch markers
I am not advocating skipping them altogether, but for a shawl knitted in the round, I will typically only use stitch markers for every segment. For instance, a square knitted in the round usually has 4 segments, so I will have 4 stitch markers.
I am currently binding off a circular shawl that has 210 patterned rows, and is 8 segments in the round. I slipped markers 1680 times, but if I had a stitch marker every 20 stitches, plus for one to mark each segment, I would be slipping markers over 6000 times.
7. Provisional cast on for Very Fine Yarns
I recommend that if you are knitting flat with very fine yarn that you consider doing a COWYAK.
One of the problems with very fine yarn is that at the beginning, it is difficult to read your knitting because there is not enough weight to stretch out the yarn a little. This means you will use your fingers to do it, which is an additional strain and will slow you down.
Using a COWYAK with a slightly heavier yarn will give you that weight at the beginning. I recommend doing at least 5 or 6 rows, maybe more, because if you do need to stretch out your knitting to read it, it will also give you a 'handle' to use.
It will not be too heavy to stress the yarn, as once it is long enough, the COWYAK will just rest on your lap.
Additionally, you will be able to bind off both sides the same way, which will look nicer.
8. Wool and Animal Fibres are Queen
Elastic fibres make it easier for decreasing. This is really important because there is so much decreasing in lace.
It is also crucial to point 4 above. Decreasing in one movement with linen or cotton is more difficult than with wool or alpaca.
9. Skip the Knitted-on Border
I know they are traditional and pretty, but they are also slow and tedious and it is like sleeve island: it happens after the rest of it is done.
10. Knit Every Day
If you work on it every day, it will be easier for you each time you pick up the project again, especially if the pattern is repeating a lot.