If by visa you mean the sticker in your passport, this visa is required to enter the US only (it basically allows you to "knock on their door and ask to come in"). If it expires while in US, you are still in valid status if your I94 (Entry/Exit Document) is valid.
If your L1 petition was (re-)approved by USCIS and your want to stay in the US longer, file for Adjustment of Status, this will extend your legal stay.
However, my understanding is that your employer did not file a new L1 petition and wants to send you to Canada now. To be allowed to have your TRV (temporary resident visa) application processed in the US, you need to have been legally admitted. Since I understand you got a 6-month I94 on your last re-entry, you should be good.
If not already done, ask your employer to submit a request for an LMIA-exemption opinion to the temporary foreign workers unit (TFWU), this would help you deal with the CBSA or Canadian consulate. see cic.gc.ca/english/work/employers/tfw-units.asp
Since I got my work permit in the intra-company transferee category last year, they have announced changes to International Mobility programs. Not sure if it's effective yet or if it affects intra-company at all. So have your employer send an email to the TFW unit serving your province of destination, asking for the requirements of C12 and an assessment request form. That will take about 3 weeks, and then you apply for your visa - if needed, depending on what country you come from, preferably online or alternatively by mail. CBSA will issue the work permit at the border.
Please try to understand that a visa is a document that is required for entry to the respective country only. What indicates your legal status once inside the respective country is a stamp, permit or other document (the only notable exception to the rule is Australia). In the case of the US, it is the I94. In Germany it is an entry stamp or electronic temporary residence entitlement card. And in Canada it is passport stamp, visitor record or work/study permit.
