Oh dear! Please dont listen to 'friends' who tell you things that upset and stress you, however well intentioned they are (just ask Cassie!!) Why people have to give 'advice' and consider it the gospel truth and expect you to act on it immediately, I dont know! We all have opinions based on our own experiences but that doesn't mean that what has happened with our mares/horses in general WILL happen to anyone elses! The words might, maybe, possibly, included in converstaion 'advice' can make things seem a lot less worrying to the person receiving the 'advice'.
Lady is looking good. She's moving well towards foaling. This is her first foal and ALL mares are different with their first ones. Yes, she could foal with no milk, but it is highly unlikely! Should this happen then for a start the foal will be fine if it has no food for 6 hours or so (people will scream at ME for saying this LOL!!) which would give you time to go an get some replacement milk - providing you have already found out where to get it from. Yes, if she has no milk then a vet would need to give her a jab to bring it it, but I am very reluctant to give these jabs BEFORE the mare foals, as so many mares seem to have little or no milk until they foal, then it floods in within hours!! Two years ago one of our maiden mares foaled with such a tiny bag that it was difficult to see (about 2" wide by 4" long and about an inch in 'depth'), but it was 'hard' from the day before she foaled. The foal was constantly at the milk bar and I worried that there was nothing worth anything available, but I waited and after 24 hours the foal steadied up on its milk search which meant that more milk was flowing, and the following day the mare had extra milk flowing out of her teats everytime the foal stopped drinking - yet her bag never got any bigger. She may be in foal for this year (July) so I await with interest to see the size of her udder this time!!
Lady still has a while to go before she foals (my opinion from your pictures) so there is still time for her to start her milk supply. But I wouldn't think she has that long, so just reminding you that she will need worming (should be approx a month before foaling) so if you haven't done this, then now would be a good time? Also have an Ivermectin wormer ready on hand to give her a dose within 12 hours of her having the foal.
So dont panic - get her wormed, get her foot trimming up to date before she gets too heavy to balance her weight comfortably, keep plenty of moisture going through her system on the run up to foaling (grass is best, but if not available then keep her food as moist as you can) plenty of space to move around in, or take her out for gentle walks - good for you as well as her!, get her a 'lick' that is specifically for breeding stock to make sure she has all the necessary minerals and vitamins she needs - now is the time to change her on to a good quality mare and foal feed if you haven't done it already. Lastly get hold of a 'just in case' foal replacer milk or find out where you can get some at a minutes notice. Oh and plan where you are going to have her foal, and make sure it is totally safe for both mare and baby - no nasty projections, closed in walls and door so Lady cant get her foot caught up if she rolls during foaling and likewise for the foal. Get organised with some bales of straw (or hay if you prefer) for bedding - shavings are not good as they stick to the foal when it is first born and the small shavings/dust can get up a foal's nostrils or in it's eyes during the weeks following foaling.
LOL!! I'd better stop my rambling or you will fall asleep before finishing reading. Good luck, do keep us all up to date with how things are progressing, and PLEASE ask any questions or simply ask for support if you are feeling a bit stressed or unsure about anything.