Negative lag is the same as a ‘lead’ and advances the scheduled start (or finish) of the successor. Most authorities do not like ‘leads’ (eg, the DCMA 14 point check list: http://www.mosaicprojects.com.au/WhitePapers/WP1088_DCMA-14-Point.pdf ) However, particularly in high-level schedules and early in the schedule development cycle making the logical statement that ‘painting’ can start 2 weeks before the finish of ‘welding’ is reasonable if both activities are several months. As the level of detail builds in the schedule real links can replace the ‘lead’.
Positive lags delay the successor activity and are generally accepted as useful provided the lag does not replace an activity. Lags can be used to represent administrative lead times, to manage work flows or to represent mandated drying, curing, setting times when nothing can happen.
Both need to be used with care and you need to understand how they are applied by your software (there’s no consistency). For ore on this see: http://www.mosaicprojects.com.au/PDF/Links_Lags_Ladders.pdf