People with this history I don't start with vanilla Starting Strength, but progress as follows. I assume a normally-equipped gym with machines, dumbbells 5-25kg in 2.5kg increments, 20kg barbell and iron plates (no bumpers or plates under 1.25kg) a bench press, and a power rack with safeties.
The keys here are building good movement skills and confidence. The person generally injured themselves from sloppy movement, either sitting at a desk for years, or lurching something around in the garden, etc. Good movement is the foundation of strength, they'll do better in terms of keeping their back healthy with a sharp 40kg squat than a sloppy 140kg squat.
Confidence is important because the person who's been injured, helpless and in pain doesn't want to go there again, and they become hyperaware of twinges and aches.
For these reasons, you start them absurdly easy and build up slowly. Microloading is good, but in a typical gym you can't do it, so you build reps instead. For example, if they bench 40kg 5x3, then next week 40kg 6x3, and so on up to 40kg 10x3, six weeks have gone by and now they will certainly be able to bench 42.5kg 5x3. Barbell squats and deadlift can build from 3 to 5 reps before adding weight, everything else from 5 to 10. In most cases 2-3 warmup sets and 3 work sets are plenty.
The exercises are done for roughly six weeks each
- Goblet squats ---> double dumbbell front squats --> barbell front squats ---> barbell low-bar back squats
- Plank ---> dumbbell bench press ---> barbell bench press ---> barbell overhead press (keeping the bench press in).
- Seated cable row alternating with lat pulldown, these two are kept in though cycles, in each new cycle drop the weight back 4 weeks and build up again, eg 60 to 72.5kg in one cycle, 62.5 to 75kg in the next, etc.
- Rack pulls from just below knee working up to 75kg ---> deadlifts starting at 60kg. After this keep the deadlifts in, but do them every second session, and as before drop back weights 4 weeks in each new cycle and build up.
- Farmer's walks --> rack carry ---> after this alternate farmer's walks, rack carries, and the deadlifts, ie DL/FW/DL/RC etc.
Really there is a lot of judgment involved in this. For example, if the person carries a lot of fat on their trunk I omit the planks, as the weight will drag on their lower back causing pain, and their belly or breasts brushing against the ground will embarrass them - see confidence mentioned above.
Nonetheless, this gives a sketch of what I do with people with significant lower back issues. The outcomes are generally good. What the person has to understand is that they will always be this way - the dodgy back is like diabetes or something, you never get rid of it, you just manage it. Strength training will not resolve these issues, it will only mitigate them, reducing the frequency and severity of flareups. These flareups will affect the person's confidence, most will quit and never get through the whole programme. But
here is a 66yo woman who did, 2.5yr after two herniated discs she has squatted 75kg, benched 30kg, and deadlifted 105kg.