Use of LrC on two PCs located on different continent.

Pease clarify. Are you trying to use the same LrC license, or are you trying to edit the same catalog?

Also, section 3.1 is pretty clear

3.1 License. Subject to your compliance with the Terms and applicable law, we hereby grant you a non-exclusive, limited, revocable right for you to install, access and use the Services and Software that we make available to you, and that you license from us. Each license is to be used by only one (1) person and cannot be shared. 

Neither needs to be logged off. However, what your proposing is a breatch of the ULA

4.4 No Transfer. YOU MAY NOT RENT, LEASE, SELL, SUBLICENSE, ASSIGN OR TRANSFER YOUR RIGHTS IN THE SOFTWARE, OR AUTHORIZE ANY PORTION OF THE SOFTWARE TO BE COPIED ONTO ANOTHER INDIVIDUAL OR LEGAL ENTITY'S COMPUTER EXCEPT AS MAY BE PERMITTED HEREIN. You may, however, transfer all your rights to use the Software to another individual or legal entity provided that: (a) you also transfer (i) this agreement, (ii) the serial number(s), the Software and all other software or hardware bundled, packaged or pre-installed with the Software, including all copies, upgrades, updates and prior versions, and (iii) all copies of font software converted into other formats to such individual or entity; (b) you retain no upgrades, updates or copies, including backups and copies stored on a computer; and (c) the receiving party accepts the terms and conditions of this agreement and any other terms and conditions under which you purchased a valid license to the Software. NOTWITHSTANDING THE FOREGOING, YOU MAY NOT TRANSFER EDUCATION, PRE-RELEASE, OR NOT FOR RESALE COPIES OF THE SOFTWARE. Prior to a transfer Adobe may require that you and the receiving party confirm in writing your compliance with this agreement, provide Adobe with information about yourselves, and register as end-users of the Software. Allow 4-6 weeks to transfer. Please visit http://www.adobe.com/support or contact Adobe's Customer Support Department for more information.