Dogs generally sort things out themselves although when there is a size difference, it can be a bit difficult (I should know!). If your smaller dog is still going back to play with the Lab each day and is actually inviting or initiating play, then I wouldn’t worry too much. Small nicks and scratches and bruises are common in rough dog play. A good idea would be not to let play sessions go on for too long or get too intense. You say the Lab lies down when you appear - that’s good, you can use that for a sort of time-out, to calm things down a bit. Interrupt them every so often, to “reset” things - and after a while, this may help the Lab moderate its play as it never gets a chance to get really hyped up. People often think that it’s mean but it’s actually not a good idea to let play get too aroused, as that’s when things can get out of hand. Often if you have 3 dogs, the older, wiser dog will tend to break the other two up every so often, as dogs themselves can recognise aroused, over-excited states and they don’t like it.
You can also try and teach your Lab the “appropriate” level of play. To do this, you will need to supervise whenever you can when they’re playing and interrrupt the play if you can see that your smaller dog is becoming overwhelmed or you see your Lab doing something that you feel is too rough. This can be as simple as a loud “Aa-aah” or a warning “Gentle, Lulu!” or a loud sudden noise, if they ignore your voice - or even asking her to lie down, if she listens to you. She’ll quickly realise that if she is too rough, play is interrupted or ceases altogether. This is how puppies teach bite inhibition to each other: if one is too rough and bites too hard, the other one squeals and walks away and the game ends. So the first puppy soon learns that unless he softens his bite & his play, he loses his playmate and the fun. This is the same way we teach young puppis to stop mouthing humans.
The key is to praise Lulu lavishly as soon as she even pauses slightly in her play or seems to be toning it down slightly, after you have warned her or interrupted her. A lot of the times, people tell dogs off for doing something but don’t praise/reward them for doing the right thing, making it very hard for the dog to learn. You have to show them “NO, don’t do this - YES, do that!”. Most dogs are responsive to praise and will repeat the actions that get them rewarded. Dogs also learn by association. So whenever you see Lulu interacting gently with your smaller dog, praise her hugely (“GOOD girl, Lulu! Well done, good girl!”) - so she starts to realise that she gets attention and praise for certain actions and negative attention for others.
Finally, you may want to consider arranging a place where your smaller dog can get away from Lulu’s attentions for a while, if she wants to. This is what is usually advised for people who bring a new puppy into a household with an older dog. It is good to always give the quieter, gentler dog a “retreat” away from the other dog, when things get too much. Perhaps have somewhere where the smaller dog can go into but Lulu can’t coz she’s bigger. If you can’t arrange this, then you may want to separate them for short periods at certain times in the day, so the smaller dog can have some peace.
This is also a good idea anyway when you have 2 dogs that live together as it helps prevent separation anxiety. Dogs should learn to stay alone for short periods, as otherwise they become too emotionally dependent on the other dog and if something should happen (eg. the other dog needs to go to the vet) - they can become very distressed and destructive. Start with short periods (for Lulu’s benefit, I know your other one was used to being an only dog before) - say 5mins, then 10, 15, 20, etc - perhaps have Lulu in one room alone and your other dog in another. If Lulu makes a fuss, barking, scratching, etc - ignore her and DO NOT release her while she is making a fuss. Wait for a pause in the racket before releasing her. Otherwise, she will think that barking/fussing, etc will get her attention and release.
Hope this helps -
[Edited to add: Also - you may like to encourage them to play with a tug toy together, rather than wrestling/biting type games as this channels their energy into pulling on the tug toy and there is less likelihood of them hurting each other. Most dogs love playing tug…you can use something as simple as a long, old towel - drag it around and one dog will probably chase and grab one end of it, the other dog will try to grab the other end - and the game is on! ]