Lightroom license allows for you to have the program active on two computers PC/Mac with one in use at any point in time. There is no activitate system like Photoshop so its up to you how you manage this process. The system requirements for Win is shown below so you will have to see if your "new surface pro meets these requirements.
Windows
- Intel® Pentium® 4 or AMD Athlon® 64 processor
- Microsoft® Windows Vista or Windows 7 with Service Pack 1 or Windows 8
- 2GB of RAM
- 1GB of available hard-disk space
- 1024x768 display