"Lor' lumme" is a contraction (eye dialect) of "Lord love me": an exclamation, like many in English, which is religious in origin but not necessarily so in usage (compare with "oh my God" or "for God's sake", which many people use casually in speech nowadays, whether they're religious or not).
"another on 'em" is a colloquial way of saying "another of them". A helpful comment from Gareth Rees cites the OED as saying "on, prep. 28. = of prep. (in various senses). Now archaic and regional" - which would fit with the (now-)archaic and regional dialect used in general for Billy Peasemarsh's speech. There are also other usages of the specific phrase "another on 'em", admittedly predating Five Children and It, in which the meaning is more clear:
‘She has no brother or sister.’
‘Niece, nevy, cousin, serwant, young ‘ooman, greengrocer.—Dash it! One or another on ‘em,’ said the turnkey, repudiating beforehand the refusal of all his suggestions.
-- Charles Dickens, Little Dorrit, Chapter 6
Tyb. That's one of the fellows who beat me last night. [...] There's another on 'em!
-- Thomas Egerton Wilks, The King's Wager
In context, then, it seems that Billy Peasemarsh is assuming Anthea, like Jane, to be "[t]ouched in the head" and talking apparent nonsense about a furry fairy that grants wishes:
'I tell you we did,' Jane said. 'There's a fairy there - all over brown fur - with ears like a bat's and eyes like a snail's, and he gives you a wish a day, and they all come true.'
'Touched in the head, eh?' said the man in a low voice, 'all the more shame to you boys dragging the poor afflicted child into your sinful burglaries.'
'She's not mad; it's true,' said Anthea; 'there is a fairy. If I ever see him again I'll wish for something for you; at least I would if vengeance wasn't wicked - so there!'
'Lor' lumme,' said Billy Peasemarsh, 'if there ain't another on 'em!'
Peasemarsh, and also the policeman who arrives shortly afterwards, both seem to assume that the boys are thieves and the girls are not quite sane: the policeman expects that the magistrate will ultimately "[s]end the afflicted ones to a home, as likely as not, and the boys to a reformatory". So Peasemarsh's remark about "another on 'em" presumably means, from his point of view, another poor crazy girl being dragged into crime by her brothers. A simpler paraphrase of his sentence might be:
Good Lord, here's another of them!