Hi there
I'm a vet in mixed practice, and can maybe offer a professional angle on this.
We do recommend worm egg counts throughout the summer to check whether the lambs need worming, but Nematodirus as mentioned can cause problems in young lambs before eggs are shed, this depends on things like the weather, and the previous year, your local vet should have an idea as to whether it is a high or low risk this year. In high risk years, we recommend a white drench through the Nematodirus risk period (again depends on weather as to exactly when this is).
Ewes and rams shouldn't need worming as often as they have a certain amount of resistance, but it is recommended to worm ewes around lambing time as they are likely to shed high numbers as the immune system is lowered around birth. Many people do this with a drench as the ewes have lambed before they go out with the lambs, or as you are catching newborn lambs in the field to check/castrate/tag, or with a longer lasting wormer just before lambing starts. Again, speak to your vet about what wormer may be best for your situation. Ewes should have poo checked for worm eggs at least once through the summer, and then again before going back to the ram, as you want them to be at full fitness, and if high, may need worming to achieve this.
Liver fluke is a different story, fluke egg checks cannot be done using regular equipment and tests, so the vets often have to send samples away, which is why checks are often more expensive. If you are in a high risk area/farm for fluke, it is recommended to treat all your sheep for fluke at certain times of year, depending what flukicide you are using, your vet should be able to advise you on this for your local area.
Resistance to wormers is becoming a big problem, so keeping worming to when it is necessary, and the lowest class of wormer that works for you (if the earliest wormers don't have resistance, the advice is to keep using them, then you have all the other kinds to move onto if there is resistance developing!). Also, if you have some stronger ewes, that have single lambs, it can be worth leaving one or two unwormed, to allow some worms onto the pasture that are not resistant, and so keep the resistant worms from multiplying.
SCOPS - sustainable control of parasites in sheep - is a very useful protocol for seeing how best to minimise resistance on your farm, and if you google it, you can see all their advice.
In terms of vaccination, if the ewes are vaccinated against clostridial diseases, then as long as they have had a booster 4-6 weeks before lambing, the lambs will have some immunity passed to them through the placenta and colostrum. As mentioned, the lambs themselves will need vaccinating twice, 4 weeks apart, from 3 weeks old, in order to stimulate their own immune system. Clostridial diseases can cause lambs to struggle to thrive, or even drop dead, so they are well worth protecting against.
Good luck with your lambing, and if in doubt, give the vet a call, they can always talk you through problems or any other questions on the phone!