It appears L&BP did contact the carriers of LM's and Judith's phones and managed to ascertain that text exchanges did take place between 1634 & 1638, though the contents were never retrieved. Concerning the retrieval of the contents of text messages -- it seems to be a grey area in the realm of telecomnunications . Some sources suggest they aren't retrievable at all, while others say they can be recovered with a court order, and others say that they can be recovered with a court order -- as long as 12 months hasn't elapsed between the times the texts were exchanged and the date on which a court order is made. I would be surprised if L&BP didn't try and recover the contents via a court order. So, what was the upshot of their application? They were too late with the application? The contents had disappeared forever and weren't able to be traced or recovered? Or they were recovered, but nothing incriminating was found (meaning LM got lucky or he, perhaps, deliberately omitted a time of their meeting because he had made up his mind that he was going to kill Jodi, consciously & cunningly protecting his own back from the inevitable murder investigation)?
As for no incriminating DNA being found on LM's phone, well, he either got lucky that no incriminating DNA transferred on to his phone (eg, his phone was well shielded and protected in one of the pockets of his army parka) or he had access to many phones and swapped the sim cards.