Nested PCR uses two round of amplification where as LAMP PCR single reaction.
In general Nested PCR uses two different set of primers;, when first round of experiment is completed, we need to open the tube and use it as a template for second reaction with second set of primer. The major drawback is higher probability for cross-contamination thereby requires skilled personnel and separate room for preparation/addition of template.
LAMP PCR - Mostly uses three set of primer pairs. All primers added in a single tube with appropriate master mix and polymerase (Bst). Here, we even don't need a thermal cycler, just a dry heat bath which maintain temperature precisely is sufficient. Usually, amplification occurs at 56-60C. Results can be visualized by naked eye observation (if HNB dyes used) or UV exposed (if SYBR or similar dyes).
Technically, LAMP is easier to perform under limited resource settings and the cost of the consumable can be reduced significantly in bulk purchase. The components used for nested PCR may appears cheaper but technically (sensitivity) inferior to LAMP.
I have experience in nested PCR (dengue) and LAMP PCR (HBV). Considering the two round of amplification, probability of cross-contamination, requirement of thermaly cycler, electrophoretic units, gel documentation system, consumables related to post PCR approaches (two electrophoresis) and time utilized (second round and two gel run) I will opt LAMP methodology.
Use HNB dyes instead of SYBR. I think you can save 5-6 fold amount by adopting this step. After successful optimization reaction can be reduced to minimal volume. You can try with ELISA plate and sealers instead of pcr plates and sealers which is costlier comparatively. If you use HNB dye it can be done easily since naked eye observation is enough to record results. Never compromise with filter tips to save cost. If you have multichannel pipette it will save time and chances of cross contamination can be reduced significantly thereby save cost. You can try with pcr strips instead of single tubes. Upto my knowledge these minor adjustments can be done without compromising results