Is there a karyotype database for human cell lines?
As far as I know and have found, there is no one master database for karyotypes of all human cell lines. They are usually grouped into subsets either by some commonality (e.g. being cancers) or simply because of who/where they were developed and how they chose to share the line. Some good databases/resources are:


ATCC - A great repository that has cell line datasheets, references, images, and culturing info. I highly recommend using ATCC as your first stop when looking to learn more about a line.
NIGMS Human Genetic Cell Repository - A very robust repository that contains far more than just cell lines. It's good, but the wealth of info can be a bit difficult to sift through.
COSMIC - A great collection of info on cell lines and mutations found within them. Good if you want to look for/understand particular genetic aspects of a line.
Cellosaurus - A fantastic database on cell lines! I particularly like the info Cellosaurus hosts on different names and common misspellings of names for cell lines. It also provides info on hierarchies of cell lines- that is, when multiple cell lines are derived from a parent line. This is super helpful when trying to parse literature with confusing references to similar lines. It also provides references and cross-references. I cannot recommend this one enough.


To get back to your particular cell line, I have only been able to find one reference to a line called 'LG2'- even with the help of the resources listed above and PubMed, so I, unfortunately, can't give you much info on that specifically. If there really is so little info on this line, I would suggest contacting the source (colleague, lab, excel sheet associated with your storage system, etc.) for your cells to see what info they have. If you can't find anything that way, it may be best to just submit a sample for sequencing yourself and get that info out there.