You can check this with some TSQL queries related to memory pressure which might tell you your SQL Server is under memory pressure (cause of that memory limit)
As a short explanation... every query needs some memory to work (e.g., working buffer, cache, resultset, sorting, versioning).
If you have just one user, everything will be fine, and if you have ten users with different queries, your SQL Server will request the ten-time amount of memory. If you have 100s of users...
so yes, your performance issue might correlate with the memory (or even - depending on the version - with compute power).
But there also might be some options to speed up your queries - with query and/or index tuning.
I recommend setting up a second instance with developer edition to test/dev a new version of your application. There you have the chance to increase the working memory to at least 2GB or 4GB (or even more).