Typically, options are assigned to the individual, and vest (mature on a schedule) with years of service to the said company that issued the options.

I believe PTSC options vest on a 3 year schedule (someone please correct me if I`m wrong. Options granted to lowell last year will only be 1/3 vested, two years ago will be 2/3 vested, etc...so the answer is yes, he does take his options with him.

Also...usually Execs can negotiate their departure to the degree (and including) of including exceptions to options and vesting schedules. It very well may also be the case that LG will get full vesting from options recently granted...

Regards