The boiling points of N-methyl-pyrrolidone (202°C) and gamma-Butyrolactone (204°C) are way too close for it to be possible to separate them by vacuum distillation. Also, take note of that the auto-ignition point of NMP is 270°C according to its MSDS1, so do NOT subject either pure NMP or a NMP/GBL mixture to excessive heat!
Thus, for separation of the two compounds, you have to resort to another scheme, and my best suggestion for this follows here. The scheme works perfect in theory, but has not to my knowledge been tested in practice by anyone, so please exercise caution, and also report back to me if you have performed this separation like suggested here, or in any other fashion for that matter.
Vigorous basic hydrolysis2 of a mixture of N-methyl-pyrrolidone and gamma-butyrolactone would create 4-hydroxybutyric acid and N-methyl-4-amino-butyric acid (N-Methyl-GABA). Mild acid treatment3 of this mixture would preferentially esterify the GHB to GBL, while still leaving the amino acid in its zwitterionic form - amides form much less readily than lactones, especially in aqueous solution. The formed GBL could then be continuously extracted from the reaction mixture4 with a water-immiscible solvent in an extraction apparatus or by allowing the mixture to cool and make a solvent extraction in a sepfunnel every 20-30 minutes until no more GBL is retrieved. Yet another alternative method would be to steam distill the GBL from the hydrolysis mixture as it forms adding water at the same rate it distills off. Finally the distillate is extracted with a water-immiscible solvent from the GBL/water mixture.
Finally, regardless of method chosen above, you now have a solution of crude GBL in a non-polar solvent, and pure GBL is isolated by drying the solution over anhydrous MgSO4 or similar, filtering, evaporating the solvent (preferably under vacuum, collect it for reuse!), followed by (fractional) vacuum distillation of the GBL (Important!). It is possible to do without vacuum, but it is a bit impractical as the bp of GBL is 204°C at atmospherical pressure - something really requiring a heating mantle. During this distillation (which is to be conducted very slowly, 1-2 drops a second), watch closely for any distillate coming over below 204°C and discard this and the first 10-15% of the GBL (as it likely contains/consists of NMP, bp 202°C - this portion is not lost however, as you can resubject it to the above separation again).
[1] MSDS: N-methyl-pyrrolidone (NMP) (http://www.astrochemicals.com/25083.pdf)
(http://www.astrochemicals.com/25083.pdf) MSDS: gamma-Butyrolactone (GBL) (http://www.astrochemicals.com/25079.pdf)
(http://www.astrochemicals.com/25079.pdf)
[2] Reflux with 2-3 molar equivalents of 30-40% aqueous NaOH or KOH for a while, maybe 1-2 h? Check Vogel's book (https://www.thevespiary.org/rhodium/Rhodium/chemistry/vogel3.html)
(https://www.thevespiary.org/rhodium/Rhodium/chemistry/vogel3.html), Organic Syntheses (http://www.orgsyn.org)
(http://www.orgsyn.org) or similar for how long a standard amide hydrolysis takes.
[3] Acidify to pH 2-3 with 25% w/w HCl or H2SO4, heating to maybe 40-50°C with good stirring.
[4] Continously shifting the GHB <-> GBL equilibrium to the right, which is around 1:1 or 1:2 in an aqueous solution.