Morecambe play at the Globe Arena, which was only completed in 2010. The ground is actually slightly closer (a 20-25 minute walk) to the station and town centre than the previous ground was. There's no parking at the ground itself, but there's plenty of street parking within a few hundred yards.

The only place to get a drink reasonably close to the ground is the bar in the Regent Caravan Park. Alternatively, particularly if you park on the east side of the ground, there's the William Mitchell which is only around a 10 minute walk from the ground. If you're making a day of it or are staying overnight then you'll probably end up drinking in the centre. In that case some options are:
The Palatine - for the beer connoisseur
Tivoli Bar - Sam Smiths, so cheap, but no hand-pulled
The Eric Bartholomew - Wetherspoons

All of the places above are marked on the pub map.
Pub map

Internet Ground Guide
The Football and Real Ale Guide