Hi Anita,
As most law firms are well aware of the prohibitive cost of research services, I doubt if any lawyer or attorney would expect you to fund research done on their behalf. Subscriptions to LexisNexis or Carswell can easily run into the hundreds of dollars per month and extend well into the thousands of dollars depending on the depth of research needed. Law firms need to maintain these subscriptions as a cost of doing business and if I were to offer such a service as a paralegal I would stipulate that the cost be directly disbursed back to the law firm.
You can read more on this thread
here and the search mechanism on this forum is a great tool. Good luck!