It's possible of course but it doesn't gain you much in terms of clarity or lines of code savings (and it also isn't faster, as LINQ isn't inherently faster than a conventional approach):
List<GlobalFieldDatabase> fin =
(from t in bg
where UserEntites.ContainsKey(t.BudgetEntityCode)
&& UserGlobalFields.ContainsKey(t.GlobalFieldCode)
select new GlobalFieldDatabase()
{
BudgetEntityId = UserEntites[t.BudgetEntityCode],
GlobalFieldId = UserGlobalFields[t.GlobalFieldCode],
GlobalFieldValue = t.GlobalFieldValue
})
.ToList();
Edit: By the above reservations I don't mean that I would advise against using LINQ here, just that there is no objective benefit and you'd have to decide yourself which approach to use based on personal preference.