Purdue and Lynchburg College have been doing a lot of recent research:

Force Attenuation Of New And Used Lacrosse Helmets
All of the helmets (Cascade Pro7, Cascade CPXR) passed the NOCSAE standard suggesting they can still adequately attenuate blows to the head, even after 3 years of use without reconditioning.

-GOOD NEWS for old Cascade helmets.

Force Attenuation Of Football And Lacrosse Helmets
Force attenuation capability, measured by GSI, varied across helmet models according to drop location after accounting for differences in sport. Overall, football helmets performed better than lacrosse helmets, and we found a wide variety of GSI scores among the different brands within each sport. Although lacrosse helmets are manufactured for a different athletic context, it may be possible for aspects of football helmet technology to be adapted to lacrosse helmets in the future in order to improve force attenuation performance.

- Not so good, but does Lacrosse need Football level protection?

Characteristics Of Football Helmets Associated With The Incidence Of Sport Related Concussion In High School Football Players
A total of 204 players (8.9%) sustained 208 SRC causing them to miss a median of14 (10.1,20.2) days. There was no difference (p = 0.773) in the incidence of SRC [SRC/ helmets, (%: 95% CI)] for players wearing Riddell [108/1172 (9.2%: 7.7,11.1)], Schutt [56/678 (8.3%: 6.4,10.7)], Xenith [40/438 (9.1%: 6.7,12.3)] helmets. There was no difference (p = 0.365) in the incidence of SRC for helmets that were used for their first and second seasons, [47/463, 10.2%: 7.6,13.4)], third and fourth seasons, (72/904, 8.0%: 6.3,10.0) or five or more seasons (83/895, 9.3%: 7.5,11.0). There was no difference (p = 0.249), in the severity of SRC for players wearing Riddell [13.0: 9.0,19.0], Schutt [14.0: 10.5,23.0] and Xenith [14.5: 11.8,19.0] helmets. There was no difference (p = 0.239) in the severity of SRC for helmets that were used in their first and second seasons [16.0: 11.0,19.5], third and fourth seasons [12.0: 8.0,21.0] or five or more seasons [13.5: 10.0,19.0].
Conclusions: Despite manufacturer’s claims, there was no difference in the incidence or severity of SRC based on the helmet brand or helmet age. ATs need to be aware that factors other than the type of football helmet may affect the risk of high school players sustaining a SRC.

- So all helmets (new, old, different brand) basically act the same in reducing concussions.