Oh Lol poor little L. Hope she gets sorted soon. It's awful watching them suffer. Plenty of water seems to do the trick here.
Quod I would say it's just a phase. E has been like that at times (and is like that at the moment - will only settle with boob and not at all for DH) and had reverted back to normal (if there is such at thing with babies) after a week or so.
Tally I think babies are generally around 3 months before their circadian rhythms develop properly so not much point trying to implement a routine before then, and then after that I think it's trial and error. Some of us have babies who respond really well to routines and others not at all. Personally I have one of the latter and trying to force her to sleep and eat at times to suit me would just lead to misery so we just followed her lead by responding to tired and hungry signs. By 5-6 months a little baby-led routine had developed on its own but it's still flexible and I don't worry if she is early or late for a nap. Don't sweat it, you will find something that works for you
One thing I will say though is to ignore these self-professed baby sleep 'experts' who tell you that your baby will sleep 7-7 every night if you follow their advice. Research shows that babies don't sleep for 12 hours at night until they are much older so the earlier you decide bedtime will be, the earlier you will be getting up the next morning. At 3 months if you put an average-sleeping baby to bed at 7pm then they will get up for the day at 5am.
Evidence-based baby sleep chart. And the research-based ISIS site is very useful
Hazle and Lilly it is definitely not a coincidence that all three of our little cherubs are fighting bedtime at the moment is it? The fact that yours are doing it as well gives me some comfort that it is a phase that will pass. I have now given up trying to put her down for daytime naps as it just doesn't happen and have reverted back to walking her around in the pushchair to get her off and it still takes her absolutely ages to nod off. Very frustrating for me but a popular move with the dog.
Janey it sounds like M loves his sleep too much nowadays to join in on the party 
Alex I hate to scare monger but E has always reliably gone to sleep with a dummy but is now point blank refusing to take it. 