I am not sure you can. LS resist is normal effectiveness not a special protection from what I have seen. Also from experimenting with the DNA of Taanab and Mandalore creatures, all effectiveness resists get 0 effectiveness no matter how much you experiment oddly enough. Not sure if this is a bug...
If some other BE's have pulled off getting LS effectiveness I'd like to know where I am messing up.
Exactly right PyscoJuggalo, the resists from Taanab and Mandalore DNA disappear into the ether, and as they're the only ones around with LS resists in the DNA, LS resists aren't possible in engineered pets at the moment.
Wild pets are another matter, but the heavily armoured, LS resist pets are too high level for twins, but you could get a couple of CL60 or less with some LS resists.
Oh, and there are Jedi out there with pets that do have high resists to your special weapons, so life's going to be interesting.