Batch edit export from lightroom
What are your export settings? You still haven't told us what pixel dimensions you are sending to the printer, so let's try approaching it from another angle. Please tell us: 1. Does your LR editing include any cropping to improve the composition, exclude undesired elements, etc.? 2. In the LR export dialog is the Resize box checked? If yes, what numbers are in the size boxes next to the Resize box? If they are pixel values, tell us only what they are. If they are inch/cm. values, tell us also what is entered into the Resolution (ppi) box.
If the answers to the above questions are negative - you are not cropping in LR and the Resize box is not ticked, then you are sending a 3744 x 5616 pixels image, more than enough for a 12x18 inch print at 300 ppi. If you want a larger print, any lab should be able to resize that for you to at least 24x36 inches and most can make it larger. However, if you want a print larger than 12x18, I would recommend resizing it in LR rather than leaving it to the lab, because its sophisticated resizing and integrated Output Sharpening are excellent.
Assuming that you are uploading an sRGB jpg to the lab, you should tell us also what Quality/Compression you have set.