Your question is not clear. Bacterial pellet that is generated by centrifugation does not "dissolve" upon adding LB growth medium. Bacteria again diffuse into the medium. Therefore, if your goal is to investigate bacterial proteins or RNA, it may be useful to wash bacteria with PBS and then proceed with isolation of proteins etc.
You can pretty much resuspend bacterial pellets in any buffer you like, depending on what you want to do with them... I'll take a guess that you want them to keep growing? Assuming you do have some antibiotics in the LB to begin with, your bacteria will obviously excrete the antibiotic resistance proteins into the growth media and you need to wash these away effectively (say 3x spin down /resuspend/spin down/...) before you add fresh media and antibiotics. LB is expensive and a pain to make up, phosphate buffer is cheap. So it's up to you but it would be economically sensible to wash with PBS....
Thank you both for your kind answers! I was unclear, i meant the freeze dryed pellet that you get from your provider, i was told to always dissolve theese in buffer before adding the LB. But i think you answered the question in any case Richard, am i right?
right - freeze dried mixtures usually contain a mixture of protectants but not necessarily buffer salts. LB is not normally buffered (unlike Terrific Broth, for example) and maybe there will be a pH change if you just chuck it into LB....so play it safe and dissolve it in a little bit of PBS as your provider suggests. As a back up try sticking an inoculating loop in the suspension and streak onto an agar plate or two - the culture will struggle at first to recover, lag time can take a while...