3G sticks sold by Tchibo usually have a netlock and since Lidl is on the same network a Lidl SIM should work. If not you're just a short board search away from unlocking instructions.
However be aware that Tchibo and Lidl both use the same network (O2), so if your dissatisfaction is related to coverage and/or performance, Lidl won't change anything.
Whether you buy a separate SIM or bundled with their 3G stick it's always the same type of SIM card for which the same voice and data tariffs apply. The only difference is that SIMs bundled with 3G sticks come with the dayflat tariff (€ 2.50 per calendar day) preactivated while the separate SIMs are on the volume-based tariff (€ 0.24/MB), but you can switch tariffs for both at any time as described at
http://prepaid-wireless-internet-acc...ge/LIDL+mobile