Yes, the Lola/Lexi story is unrealistic, and Eastenders have already been in trouble for it. Social Workers complained when it started because they considered the behaviour of Lola's Social Worker (which is central to how the whole storyline started) totally unrealistic and inappropriate - to the extent that she'd have been disciplined long before now if it was real life.
I saw an interview where they dragged out a Soap writer (not an Eastenders writer - they were running scared of any criticism) to answer questions, and she came out with the old "the audience are intelligent enough to know it's fiction" line, but for me this just doesn't cut it. Soap writers are continually trying to have their cake and eat it: they want to prove themselves as imaginitive writers, but they have to deal with the fact that most people watch soaps (as opposed to other drama) because it's supposed to be anchored in real life. For me, the Lola storyline is comparable to - for example - an episode of Casualty where the writers invented a new disease or treatment.
What's I think is becoming increasingly clear is that the storyline so far is just a means to an end: I can't be certain, of course, but it looks to me like they're setting-up a "Mitchell's divided" storyline, with Phil trying to cut Lola out completely and adopt Lexi himself...